{"id":8,"date":"2023-09-17T11:15:57","date_gmt":"2023-09-17T11:15:57","guid":{"rendered":"https:\/\/mathority.org\/pt\/funcao-irracional-ou-radical\/"},"modified":"2023-09-17T11:15:57","modified_gmt":"2023-09-17T11:15:57","slug":"funcao-irracional-ou-radical","status":"publish","type":"post","link":"https:\/\/mathority.org\/pt\/funcao-irracional-ou-radical\/","title":{"rendered":"Fun\u00e7\u00e3o irracional ou fun\u00e7\u00e3o radical"},"content":{"rendered":"<p>Esta p\u00e1gina explica o que \u00e9 uma fun\u00e7\u00e3o irracional, tamb\u00e9m chamada de fun\u00e7\u00e3o radical, bem como todas as caracter\u00edsticas deste tipo de fun\u00e7\u00e3o. Voc\u00ea tamb\u00e9m descobrir\u00e1 como calcular o dom\u00ednio de fun\u00e7\u00f5es radicais ou irracionais e, al\u00e9m disso, poder\u00e1 ver como represent\u00e1-las em um gr\u00e1fico com exemplos e praticar com exerc\u00edcios e problemas resolvidos passo a passo. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-una-funcion-irracional-o-radical\"><\/span> O que \u00e9 uma fun\u00e7\u00e3o irracional (ou radical)?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Uma fun\u00e7\u00e3o irracional significa a mesma coisa que uma fun\u00e7\u00e3o radical e, portanto, compartilham uma defini\u00e7\u00e3o: <\/p>\n<div style=\"background:linear-gradient(to bottom, #FFFFFF 0%, #FFE0B2 100%); padding-top: 23px; padding-bottom: 0.5px; padding-right: 30px; padding-left: 30px; border: 2px dashed #FF9B28; border-radius:20px;\">\n<p style=\"text-align:left\"> Uma <strong>fun\u00e7\u00e3o irracional<\/strong> , tamb\u00e9m chamada <strong>de fun\u00e7\u00e3o radical<\/strong> , \u00e9 uma fun\u00e7\u00e3o que possui a vari\u00e1vel independente x sob o s\u00edmbolo de uma raiz.<\/p>\n<\/div>\n<p> Como j\u00e1 sabemos, o resultado de uma raiz pode ser positivo ou negativo. Assim, a representa\u00e7\u00e3o de uma fun\u00e7\u00e3o irracional (ou radical) tem duas curvas poss\u00edveis: <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/exemples-de-fonctions-irrationnelles-ou-radicales.webp\" alt=\"exemplos de fun\u00e7\u00f5es irracionais ou radicais\" class=\"wp-image-177\" width=\"430\" height=\"366\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p> Mas se o sinal n\u00e3o for especificado, a fun\u00e7\u00e3o positiva dever\u00e1 ser representada.<\/p>\n<p> Por outro lado, uma fun\u00e7\u00e3o irracional n\u00e3o deve ser confundida com uma fun\u00e7\u00e3o racional. Embora tenham nomes muito semelhantes, s\u00e3o dois tipos de fun\u00e7\u00f5es completamente diferentes. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"dominio-de-una-funcion-irracional-o-radical\"><\/span> Dom\u00ednio de uma fun\u00e7\u00e3o irracional ou radical<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> O dom\u00ednio de uma fun\u00e7\u00e3o com ra\u00edzes depende da paridade do \u00edndice raiz, ou seja, depende se o \u00edndice radical \u00e9 par ou \u00edmpar. <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"dominio-de-una-funcion-con-raiz-de-indice-par\"><\/span> Dom\u00ednio de uma fun\u00e7\u00e3o com raiz de \u00edndice par<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> Como voc\u00ea bem sabe, n\u00e3o existe raiz (\u00edndice par) de um n\u00famero negativo. Portanto, <strong>uma fun\u00e7\u00e3o radical com \u00edndice par existir\u00e1 enquanto seu conte\u00fado for igual ou maior que 0.<\/strong><\/p>\n<p> Como exemplo, vejamos como \u00e9 calculado o dom\u00ednio da seguinte fun\u00e7\u00e3o radical ou irracional:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-624a36ddc41727915170ad84e04af5f3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\sqrt{x-4}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"114\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Esta \u00e9 uma fun\u00e7\u00e3o de \u00edndice par radical, portanto devemos observar quando seu conte\u00fado \u00e9 positivo ou zero <strong>:<\/strong><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f6f54cf39cf142946b7fb5d6066009c8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x-4\\ge 0\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"73\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p> Resolvemos a desigualdade:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3bdacfb2a15271cdd2fb04176f683713_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x\\ge 4\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"43\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p> Portanto a fun\u00e7\u00e3o existir\u00e1 sempre que x for maior ou igual a 4, e \u00e9 indicada pelo seguinte intervalo: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-87a6beff3b91d11f1d2dc420d6dace7d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Dom } f= [4,+\\infty)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"137\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"dominio-de-una-funcion-con-raiz-de-indice-impar\"><\/span> Dom\u00ednio de uma fun\u00e7\u00e3o com raiz de \u00edndice \u00edmpar<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> Fun\u00e7\u00f5es irracionais com \u00edndice \u00edmpar n\u00e3o apresentam esse problema, pois existe a raiz do \u00edndice \u00edmpar de um n\u00famero negativo:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c3abab45564c61124c12eb0ffa89b7fd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\sqrt[3]{-8}=-2\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"82\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p> Portanto, existem fun\u00e7\u00f5es radicais de \u00edndice \u00edmpar para qualquer valor de <em>x<\/em> . Ou, em outras palavras, <strong>o dom\u00ednio consiste apenas em n\u00fameros reais<\/strong> .<\/p>\n<p> Por exemplo, calcularemos o dom\u00ednio de defini\u00e7\u00e3o da seguinte fun\u00e7\u00e3o radical cujo \u00edndice \u00e9 \u00edmpar:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-65987eff0c48ff229a59c03e8164c3df_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\sqrt[3]{3x-4}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"124\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Por ser uma fun\u00e7\u00e3o irracional com \u00edndice \u00edmpar, seu dom\u00ednio consiste em n\u00fameros reais: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4f565027fd5d2a4381e3a23d183c9f76_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Dom } f= \\mathbb{R}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"90\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"como-representar-una-funcion-irracional-o-radical\"><\/span> Como representar uma fun\u00e7\u00e3o irracional ou radical<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Vamos ver como representar uma fun\u00e7\u00e3o com ra\u00edzes em um gr\u00e1fico usando um exemplo.<\/p>\n<ul>\n<li> Trace a seguinte fun\u00e7\u00e3o radical ou irracional em um gr\u00e1fico:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2643f318c5e502f2d6827ec22d20f6c8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\sqrt{x+2}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"114\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> A primeira coisa a fazer \u00e9 encontrar o dom\u00ednio da fun\u00e7\u00e3o. Por ser uma raiz quadrada, tudo o que cont\u00e9m deve ser positivo, pois n\u00e3o existe raiz quadrada de um n\u00famero negativo. Portanto, a fun\u00e7\u00e3o radical existir\u00e1 enquanto seu conte\u00fado for igual ou maior que 0:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1ebfe7e55e1e5753b26b6db52894aae5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x+2\\ge 0\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"73\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-db8c8201f5940b1d818d122820973504_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x\\ge -2\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"56\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p> Assim, o dom\u00ednio da fun\u00e7\u00e3o consiste em todos os n\u00fameros maiores ou iguais a -2. Isso \u00e9 para dizer:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-fd7f6030f8b7a92cdcc6b7f9dbb34d16_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Dom } f = [-2,+\\infty)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"151\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Depois de conhecermos o dom\u00ednio da fun\u00e7\u00e3o, criamos uma tabela de valores. Obviamente, quanto mais pontos calcularmos, mais precisa ser\u00e1 a representa\u00e7\u00e3o da fun\u00e7\u00e3o. Mas calcular 3 ou 4 pontos no intervalo do dom\u00ednio \u00e9 suficiente: <\/p>\n<div class=\"wp-block-columns is-layout-flex wp-container-307\">\n<div class=\"wp-block-column is-layout-flow\">\n<ul>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a3c3800751119915b939b96fe53b0a62_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= -2 \\ \\longrightarrow \\ f(-2)=\\sqrt{-2+2}= 0\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"278\" style=\"vertical-align: -5px;\"><\/p>\n<\/li>\n<\/ul>\n<ul>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-77f388ade5bdbca831436e5786a04c02_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= -1 \\ \\longrightarrow \\ f(-1)=\\sqrt{-1+2}= 1\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"277\" style=\"vertical-align: -5px;\"><\/p>\n<\/li>\n<\/ul>\n<ul>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-30da4ca4b03a3f86d0bf78f951418371_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= 2 \\ \\longrightarrow \\ f(2)=\\sqrt{2+2}= 2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"236\" style=\"vertical-align: -5px;\"><\/p>\n<\/li>\n<\/ul>\n<ul>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a515902ef92cb39fa2cdcddba8195174_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= 7 \\ \\longrightarrow \\ f(7)=\\sqrt{7+2}= 3\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"237\" style=\"vertical-align: -5px;\"><\/p>\n<\/li>\n<\/ul>\n<\/div>\n<div class=\"wp-block-column is-layout-flow\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c72f72e58a4aa07f85403ae5717df70c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c|c} x &amp; f(x) \\\\ \\hline -2 &amp; 0 \\\\ -1 &amp; 1 \\\\ 2 &amp; 2 \\\\ 7 &amp; 3 \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"112\" width=\"90\" style=\"vertical-align: -51px;\"><\/p>\n<\/p>\n<\/div>\n<\/div>\n<p> Representamos agora os pontos obtidos em um gr\u00e1fico <strong>:<\/strong> <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/comment-representer-une-fonction-radicale-ou-irrationnelle.webp\" alt=\"como representar uma fun\u00e7\u00e3o radical ou irracional\" class=\"wp-image-178\" width=\"460\" height=\"249\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p> E finalmente, juntamos os pontos e estendemos a curva para indicar que a fun\u00e7\u00e3o continua a crescer: <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/exemple-de-representation-graphique-d-une-fonction-radicale-ou-irrationnelle.webp\" alt=\"exemplo de representa\u00e7\u00e3o gr\u00e1fica de uma fun\u00e7\u00e3o radical ou irracional\" class=\"wp-image-179\" width=\"460\" height=\"251\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-funciones-irracionales-o-radicales\"><\/span>Exerc\u00edcios resolvidos sobre fun\u00e7\u00f5es irracionais ou radicais<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3 class=\"wp-block-heading\"> Exerc\u00edcio 1<\/h3>\n<p> Encontre o dom\u00ednio da seguinte fun\u00e7\u00e3o radical: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5227797e1a51357e63fe97f3be067f96_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\sqrt{3x+6}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"64\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>Veja a solu\u00e7\u00e3o<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> A raiz quadrada de um n\u00famero negativo n\u00e3o existe. Portanto, a fun\u00e7\u00e3o existir\u00e1 quando o argumento raiz for positivo ou zero: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5c62658062f5e3d6cb16c0ee363bbd93_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"3x+6 \\ge 0\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"82\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7daaaaa8dbd463d1fd48238c117d907a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"3x \\ge -6\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"66\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f260f939524d3b3ebc56682e50ea20d9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x \\ge \\cfrac{-6}{3}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"67\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-618af1663a2fcefe0c8e7e008636a5dd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x \\ge -2\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"56\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-962c0025662fc501e1896d80160964a0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\mathbf{Dom } \\ \\bm{f = [-2,+\\infty)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"156\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">Exerc\u00edcio 2<\/h3>\n<p> Encontre o dom\u00ednio da seguinte fun\u00e7\u00e3o irracional: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-78ebc335a724fd652684605114abf8b7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\sqrt{-x+2}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"69\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>Veja a solu\u00e7\u00e3o<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> A raiz quadrada de um n\u00famero negativo n\u00e3o tem solu\u00e7\u00e3o real. Portanto, a fun\u00e7\u00e3o existir\u00e1 enquanto o conte\u00fado da raiz for positivo ou zero: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-33a4820b3d1a0ba845425a092bbc9382_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-x+2\\ge 0\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"86\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d0d57b00f0f063ba60525c7bb003c93c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-x\\ge -2\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"69\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-007ba44659e7cdccd6ee0d929da8891c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x\\le\\cfrac{-2}{-1}=2\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"98\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Lembre-se que se numa inequa\u00e7\u00e3o mudarmos os lados de um n\u00famero negativo que se multiplica ou divide, devemos tamb\u00e9m rodar o sinal da inequa\u00e7\u00e3o. <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-76d696873565b2fde467626265440add_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x\\le2\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"42\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6fcd2f8dbe5bf6b1804f522f82984da6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\mathbf{Dom } \\ \\bm{f = (-\\infty,2]}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"141\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">Exerc\u00edcio 3<\/h3>\n<p> Trace a seguinte fun\u00e7\u00e3o irracional em um gr\u00e1fico: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-42e79b66433070221b9b45119683a97f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)= \\sqrt{x-1}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"114\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>Veja a solu\u00e7\u00e3o<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Primeiramente devemos calcular o dom\u00ednio da fun\u00e7\u00e3o: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2e968b1016def57c4944997419ec6300_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x-1\\ge 0\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"73\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1f077fdba5fb39bebecba8de762e4880_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x\\ge 1\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"42\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-35d3f547259a5d3839f9d66a31e485ff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Dom } f = [1,+\\infty)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"137\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Agora criamos um array de valores fornecendo os valores da fun\u00e7\u00e3o no intervalo do dom\u00ednio: <\/p>\n<div class=\"wp-block-columns is-layout-flex wp-container-310\">\n<div class=\"wp-block-column is-layout-flow\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ce58b7b43358163474680c4ed1f679cd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= 1 \\ \\longrightarrow \\ f(1)= \\sqrt{1-1}=0\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"237\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f1aeb989c9085de4b81624b2d9fe0720_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= 2 \\ \\longrightarrow \\ f(2)= \\sqrt{2-1}=1\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"236\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-299894d9a0673df30ca5d1b163cf81be_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= 5 \\ \\longrightarrow \\ f(5)= \\sqrt{5-1}=2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"236\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3a624bf18490395896c06b5db90612d8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= 10 \\ \\longrightarrow \\ f(10)= \\sqrt{10-1}=3\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"263\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<\/div>\n<div class=\"wp-block-column is-layout-flow\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-81644903e1958606867b0908817c091f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c|c} x &amp; f(x) \\\\ \\hline 1 &amp; 0 \\\\ 2 &amp; 1 \\\\ 5 &amp; 2 \\\\ 10 &amp; 3 \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"112\" width=\"85\" style=\"vertical-align: -51px;\"><\/p>\n<\/p>\n<\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Por fim, tra\u00e7amos os pontos e tra\u00e7amos a fun\u00e7\u00e3o no gr\u00e1fico: <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/exercice-resolu-pas-a-pas-de-fonction-irrationnel-ou-radical.webp\" alt=\"exerc\u00edcio resolvido passo a passo de uma fun\u00e7\u00e3o irracional ou radical\" class=\"wp-image-180\" width=\"415\" height=\"204\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\"> Exerc\u00edcio 4<\/h3>\n<p> Fa\u00e7a um gr\u00e1fico da seguinte fun\u00e7\u00e3o irracional ou radical: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7d19c800dc2ea20793710ebeb44c57b0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)= -2\\sqrt{x}+3\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"136\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>Veja a solu\u00e7\u00e3o<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Primeiramente devemos calcular o dom\u00ednio da fun\u00e7\u00e3o: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-46bb299f47d94e1927057d14ab78801f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x\\ge 0\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"43\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4352746a25b5189ba00c16a9f10e0316_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Dom } f = [0,+\\infty)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"137\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Agora criamos um array de valores fornecendo os valores da fun\u00e7\u00e3o no intervalo do dom\u00ednio: <\/p>\n<div class=\"wp-block-columns is-layout-flex wp-container-313\">\n<div class=\"wp-block-column is-layout-flow\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-020d59f29830e2ad11c40318ae4ce5a1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= 0 \\ \\longrightarrow \\ f(0)= -2\\sqrt{0}+3=3\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"259\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-cb8b754408ffc7676b63c1a9524aca0a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= 1 \\ \\longrightarrow \\ f(1)= -2\\sqrt{1}+3=1\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"258\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-499ba530ff14f35ff3376bc0c5b8a7d2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= 4 \\ \\longrightarrow \\ f(4)= -2\\sqrt{4}+3=-1\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"272\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-57008deb14e81aa3ee6ee1546369db77_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= 9 \\ \\longrightarrow \\ f(9)= -2\\sqrt{9}+3=-3\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"273\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<\/div>\n<div class=\"wp-block-column is-layout-flow\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-01738dd5c857391ebbe824cd2d68b276_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c|c} x &amp; f(x) \\\\ \\hline 0 &amp; 3 \\\\ 1 &amp; 1 \\\\ 4 &amp; -1 \\\\ 9 &amp; -3 \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"112\" width=\"78\" style=\"vertical-align: -51px;\"><\/p>\n<\/p>\n<\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Por fim, plotamos os pontos e desenhamos a fun\u00e7\u00e3o no gr\u00e1fico: <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/exemple-du-graphe-d-une-fonction-irrationnelle-ou-radicale.webp\" alt=\"exerc\u00edcio resolvido passo a passo de uma fun\u00e7\u00e3o irracional ou radical\" class=\"wp-image-181\" width=\"408\" height=\"318\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\"> Exerc\u00edcio 5<\/h3>\n<p> Fa\u00e7a um gr\u00e1fico da seguinte fun\u00e7\u00e3o irracional ou radical: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9ba5f342391543ebd4936bdb4172b560_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)= \\sqrt{-x+5}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"128\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>Veja a solu\u00e7\u00e3o<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Antes de tra\u00e7ar a fun\u00e7\u00e3o, precisamos calcular o dom\u00ednio da fun\u00e7\u00e3o: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2ea058d741d4f54988266eff83ac4e5f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-x+5\\ge 0\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"86\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-edc9aa58baf5d190aaa50260d2682248_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-x\\ge -5\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"69\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b853f76c54b3edc8fb67cee4bc3f9e19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x\\le\\cfrac{-5}{-1}=5\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"98\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Lembre-se que se numa desigualdade mudarmos os lados de um n\u00famero negativo que se multiplica ou divide, devemos tamb\u00e9m mudar o sinal da desigualdade. <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-db032fd3a93ada954d57503dc023099a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x\\le5\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"42\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d1520ce14f7045b93c7340d4b46a1b74_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Dom } f = (-\\infty,5]\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"136\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Agora constru\u00edmos uma tabela de valores avaliando a fun\u00e7\u00e3o em pontos que pertencem ao dom\u00ednio da fun\u00e7\u00e3o: <\/p>\n<div class=\"wp-block-columns is-layout-flex wp-container-316\">\n<div class=\"wp-block-column is-layout-flow\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-cf3230433fe57141824a374833dcdf9f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= 5 \\ \\longrightarrow \\ f(5)=\\sqrt{-5+5}=0\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"250\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-16a363047ab5b63a636ceba2bc2edfa2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= 4 \\ \\longrightarrow \\ f(4)=\\sqrt{-4+5}=1\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"249\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-52fb9488589ffa8e992e1e02c27c3066_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= 1 \\ \\longrightarrow \\ f(1)=\\sqrt{-1+5}=2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"249\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-440c1e8970256a70d4e1c006720ea9fb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= -4 \\ \\longrightarrow \\ f(-4)=\\sqrt{-(-4)+5}=3\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"308\" style=\"vertical-align: -6px;\"><\/p>\n<\/p>\n<\/div>\n<div class=\"wp-block-column is-layout-flow\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8f28bfe1c88172869773c3a4baec94ca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c|c} x &amp; f(x) \\\\ \\hline 5 &amp; 0 \\\\ 4 &amp; 1 \\\\ 1 &amp; 2 \\\\ -4 &amp; 3 \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"112\" width=\"90\" style=\"vertical-align: -51px;\"><\/p>\n<\/p>\n<\/div>\n<\/div>\n<p class=\"has-text-align-left\"> E por fim, basta representar os pontos e pintar a fun\u00e7\u00e3o no gr\u00e1fico: <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/exercices-resolus-de-fonctions-radicales-ou-irrationnelles.webp\" alt=\"exerc\u00edcios determinados de fun\u00e7\u00f5es radicais ou irracionais\" class=\"wp-image-182\" width=\"363\" height=\"198\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\"> Exerc\u00edcio 6<\/h3>\n<p> Trace a seguinte fun\u00e7\u00e3o irracional ou radical em um gr\u00e1fico: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5532cd3ca43ebdac3ce43c046e15bfc1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)= \\sqrt{x^2-5x+4}\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"163\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>Veja a solu\u00e7\u00e3o<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Devemos primeiro calcular o dom\u00ednio da fun\u00e7\u00e3o:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f79b0c3812612b665aaef39de9d97149_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^2-5x+4\\ge 0\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"122\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Neste caso, obtivemos uma desigualdade de segundo grau, ent\u00e3o precisamos aplicar a f\u00f3rmula das equa\u00e7\u00f5es quadr\u00e1ticas para resolv\u00ea-la: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-bd0f7a0d21b888b4e5016eb027b534a7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=\\cfrac{-b\\pm \\sqrt{b^2-4ac}}{2a}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"165\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3e5bc09c561e2790b1af96a618a015a0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle x=\\cfrac{-(-5)\\pm \\sqrt{(-5)^2-4\\cdot 1\\cdot 4}}{2\\cdot 1} = \\cfrac{5\\pm 3}{2} =\\begin{cases} 4 \\\\[2ex] 1 \\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"365\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Dividimos a linha em tr\u00eas peda\u00e7os com as ra\u00edzes obtidas: <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/domaine-dune-fonction-irrationnelle.webp\" alt=\"\" class=\"wp-image-183\" width=\"366\" height=\"43\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p class=\"has-text-align-left\"> E substitu\u00edmos um n\u00famero por cada se\u00e7\u00e3o da desigualdade, para ver quais se\u00e7\u00f5es satisfazem a desigualdade e, portanto, pertencem ao dom\u00ednio:<\/p>\n<p class=\"ql-center-displayed-equation\" style=\"line-height: 137px;\"><span class=\"ql-right-eqno\"> &nbsp; <\/span><span class=\"ql-left-eqno\"> &nbsp; <\/span><\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c9c9c5a39dc152cdcb902dbf0b2e5b59_l3.png\" height=\"137\" width=\"680\" class=\"ql-img-displayed-equation quicklatex-auto-format\" alt=\"x^2-5x+4\\ge 0 \\ \\xrightarrow{x\\ = \\ 0} <span class=&quot;ql-right-eqno&quot;>   <\/span><span class=&quot;ql-left-eqno&quot;>   <\/span><img src=&quot;https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7c214e08b91825263231bc6eddbbdee1_l3.png&quot; height=&quot;54&quot; width=&quot;404&quot; class=&quot;ql-img-displayed-equation quicklatex-auto-format&quot; alt=&quot;\\[0^2-5\\cdot 0+4\\ge 0 \\ \\longrightarrow \\ 4\\ge 0 $ \u2705$x^2-5x+4\\ge 0 \\ \\xrightarrow{x\\ = \\ 2}\\]&quot; title=&quot;Rendered by QuickLaTeX.com&quot;\/> 2^2-5\\cdot 2+4\\ge 0 \\ \\longrightarrow \\ -10\\ \\cancel{\\ge } \\ 0&#8243; title=&#8221;Rendered by QuickLaTeX.com&#8221;><\/p>\n<\/p>\n<p>\u274c<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2ba275d878055060d9f1f232b43b8d7e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^2-5x+4\\ge 0 \\ \\xrightarrow{x\\ = \\ 5}\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"179\" style=\"vertical-align: -3px;\"><\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-83bcc8fb2e8f22a2156cd258de5ed608_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"5^2-5\\cdot 5+4\\ge 0 \\ \\longrightarrow \\ 4\\ge 0\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"224\" style=\"vertical-align: -3px;\"><\/p>\n<p> \u2705<\/p>\n<p class=\"has-text-align-left\"> Assim, as se\u00e7\u00f5es que respeitam a desigualdade s\u00e3o as dos lados: <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/domaine-dune-fonction-radicale.webp\" alt=\"\" class=\"wp-image-184\" width=\"366\" height=\"46\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p class=\"has-text-align-left\"> O dom\u00ednio da fun\u00e7\u00e3o \u00e9 portanto:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b680e7160227605450a9e97fbb9fdbbe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Dom } f = (-\\infty,1]\\cup [4,+\\infty)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"217\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Depois de calcularmos o dom\u00ednio da fun\u00e7\u00e3o, constru\u00edmos uma tabela de valores fornecendo os valores da fun\u00e7\u00e3o no intervalo do dom\u00ednio: <\/p>\n<div class=\"wp-block-columns is-layout-flex wp-container-319\">\n<div class=\"wp-block-column is-layout-flow\" style=\"flex-basis:66.66%\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ed6d482c8f20a711c2ebd8918c7b5dfa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= 1 \\ \\longrightarrow \\ f(1)=\\sqrt{1^2-5\\cdot 1+4} =0\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"296\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9d4966cf27f0fd7cbcb9897457ef1a23_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= 0 \\ \\longrightarrow \\ f(0)=\\sqrt{0^2-5\\cdot 0+4} =2\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"295\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8fc83308a6420951633f086998077ebf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= -1 \\ \\longrightarrow \\ f(-1)=\\sqrt{(-1)^2-5\\cdot (-1)+4} =3,16\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"408\" style=\"vertical-align: -6px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8887531a085876374823e623a2338970_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= 4 \\ \\longrightarrow \\ f(4)=\\sqrt{4^2-5\\cdot 4+4} =0\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"296\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6a02aa9fba40d0611a9956aa2bbb90a2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= 5 \\ \\longrightarrow \\ f(5)=\\sqrt{5^2-5\\cdot 5+4} =2\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"295\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f4f3e0f153312d18d1e053903d0ebf29_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= 6 \\ \\longrightarrow \\ f(6)=\\sqrt{6^2-5\\cdot 6+4} =3,16\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"322\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<\/div>\n<div class=\"wp-block-column is-layout-flow\" style=\"flex-basis:33.33%\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f930838c6e44ca715b85a73fafe248c6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c|c} x &amp; f(x) \\\\ \\hline 1 &amp; 0 \\\\ 0 &amp; 2 \\\\ -1 &amp; 3,16 \\\\ 4 &amp; 0 \\\\ 5 &amp; 2 \\\\ 6 &amp; 3,16 \\\\ \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"156\" width=\"90\" style=\"vertical-align: -73px;\"><\/p>\n<\/p>\n<\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Por fim, representamos os pontos obtidos no gr\u00e1fico e tra\u00e7amos a fun\u00e7\u00e3o: <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/graphique-de-fonction-irrationnelle-ou-radicale-dindice-pair.webp\" alt=\"gr\u00e1fico de uma fun\u00e7\u00e3o irracional ou radical com \u00edndice par\" class=\"wp-image-185\" width=\"482\" height=\"269\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\"> Exerc\u00edcio 7<\/h3>\n<p> Represente no gr\u00e1fico a seguinte fun\u00e7\u00e3o formada por uma raiz: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-33e1d80dd68d184dbbf07e090b2a3075_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)= \\sqrt[3]{x}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"85\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>Veja a solu\u00e7\u00e3o<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> \u00c9 uma fun\u00e7\u00e3o irracional cuja raiz possui \u00edndice \u00edmpar, portanto o dom\u00ednio da fun\u00e7\u00e3o consiste em n\u00fameros reais:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0cd1539b66edeb38040ed80168e1fd9b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Dom } f = \\mathbb{R}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"90\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Podemos, portanto, tomar qualquer ponto para criar a tabela de valores. Neste caso procuraremos muitos pontos porque \u00e9 uma raiz c\u00fabica: <\/p>\n<div class=\"wp-block-columns is-layout-flex wp-container-322\">\n<div class=\"wp-block-column is-layout-flow\" style=\"flex-basis:66.66%\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ff9cf5879c32e2787a6747b41c5ecded_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= 0 \\ \\longrightarrow \\ f(0)= \\sqrt[3]{0} = 0\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"207\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-16c416c17e3dcab315ee160cd292c972_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= 0,5 \\ \\longrightarrow \\ f(0,5)= \\sqrt[3]{0,5} = 0,79\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"283\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b97f2e3514a83904a1fd4a4fa37ef39a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= -0,5 \\ \\longrightarrow \\ f(-0,5)= \\sqrt[3]{-0,5} = -0,79\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"338\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-567dfcce97fc79b8ec915adabcf51c53_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= 1 \\ \\longrightarrow \\ f(1)= \\sqrt[3]{1} = 1\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"206\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-37cc895c2772cf32732f3ad7d5910aee_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= -1 \\ \\longrightarrow \\ f(-1)= \\sqrt[3]{-1} = -1\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"261\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2cd85b49489d08da13490ab97bdf708a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= 8 \\ \\longrightarrow \\ f(8)= \\sqrt[3]{8} = 2\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"206\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-438025444e3289620b8a5bf11d39660b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= -8 \\ \\longrightarrow \\ f(-8)= \\sqrt[3]{-8} = -2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"261\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<\/div>\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow\" style=\"flex-basis:33.33%\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-21eb0a68ee7f4b9bc5c5fb42f5a36328_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c|c} x &amp; f(x) \\\\ \\hline 0 &amp; 0 \\\\ 0,5 &amp; 0,79 \\\\ -0,5 &amp; -0,79 \\\\ 1 &amp; 1 \\\\ -1 &amp; -1 \\\\ 8 &amp; 2 \\\\ -8 &amp; -2 \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"178\" width=\"121\" style=\"vertical-align: -84px;\"><\/p>\n<\/p>\n<\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Por fim, tra\u00e7amos os pontos encontrados e tra\u00e7amos a fun\u00e7\u00e3o no gr\u00e1fico: <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/representation-graphique-dune-fonction-irrationnelle-ou-radicale-dun-indice-impair.webp\" alt=\"representar graficamente uma fun\u00e7\u00e3o irracional ou radical com um \u00edndice \u00edmpar\" class=\"wp-image-186\" width=\"561\" height=\"270\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\"> Exerc\u00edcio 8<\/h3>\n<p> Resolva o seguinte problema relacionado a fun\u00e7\u00f5es irracionais (ou radicais):<\/p>\n<p> O consumo da bateria de um celular \u00e9 dado pela seguinte fun\u00e7\u00e3o:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-88e0a642418314faa4ff395e40da9dec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(t)=\\sqrt{x-K \\vphantom{(-K)}}\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"121\" style=\"vertical-align: -6px;\"><\/p>\n<\/p>\n<p> Onde o consumo \u00e9 expresso em miliamperes (mA) e<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b4e3cbf5d4c5c6d9b702dd139f14c147_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"t\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"6\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u00e9 o tempo decorrido em minutos.<\/p>\n<p> Determine o valor da constante<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ea9c87a513e4a72624155d392fae86e2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"K\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"16\" style=\"vertical-align: 0px;\"><\/p>\n<p> para que ap\u00f3s 4 minutos o consumo seja de 35 mA. <\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>Veja a solu\u00e7\u00e3o<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Que ap\u00f3s 4 minutos o consumo seja de 35 mA significa que quando t \u00e9 4, f(t) \u00e9 35. Ent\u00e3o f(4)=35. <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-60a9c6e6fc25b6b4a22742383a429400_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(4)=\\sqrt{4-K} = 35\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"159\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-59baad76cb4a8eeb877d6eb6055c6777_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\sqrt{4-K} = 35\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"101\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Agora precisamos resolver a equa\u00e7\u00e3o que obtivemos. Se voc\u00ea olhar de perto, \u00e9 uma equa\u00e7\u00e3o irracional, pois tem uma raiz. Neste tipo de equa\u00e7\u00f5es a primeira coisa a fazer \u00e9 isolar a raiz de um lado, que neste caso j\u00e1 est\u00e1 isolada. Uma vez isolados, devemos elevar ambos os lados da equa\u00e7\u00e3o ao quadrado:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0b834c1688aa5e4ccc87f5a2dbb56a43_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left( \\sqrt{4-K} \\right)^2= 35^2\" title=\"Rendered by QuickLaTeX.com\" height=\"27\" width=\"132\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Ent\u00e3o simplificamos a raiz:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0396a3e2a3ee507199b1b81ea70fa36a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"4-K= 35^2\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"95\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> E resolvemos a equa\u00e7\u00e3o: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7b73ab2e0cee4a13fdb21093ea88bf55_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"4-K= 1125\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"105\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e34f99c25a171ff3872dad7a5c02e577_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"4-1225=K\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"106\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f14e731da093f1ad6b0efaf13be99481_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{-1221=K}\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"88\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Finalmente, em equa\u00e7\u00f5es irracionais, as solu\u00e7\u00f5es devem ser verificadas. Devemos, portanto, substituir K=-1221 na equa\u00e7\u00e3o do in\u00edcio: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3e9b1d8c0d5969edc8e00ca5fdb7e694_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\sqrt{4-K} = 35 \\ \\xrightarrow{K \\ = \\ -1221} \\ \\sqrt{4-(-1221)} = 35\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"360\" style=\"vertical-align: -6px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-494a9f97e9765f9f23e73d2ac480e5b1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\sqrt{4+1221} = 35\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"120\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-434d3da36cdf2a90de20d45530759b9f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\sqrt{1225} = 35\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"90\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6dc9c0d5a5bb963b5a3e50a78967accc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"35 = 35\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"58\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Como a igualdade \u00e9 satisfeita, K=-1221 \u00e9 uma solu\u00e7\u00e3o.<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Esta p\u00e1gina explica o que \u00e9 uma fun\u00e7\u00e3o irracional, tamb\u00e9m chamada de fun\u00e7\u00e3o radical, bem como todas as caracter\u00edsticas deste tipo de fun\u00e7\u00e3o. Voc\u00ea tamb\u00e9m descobrir\u00e1 como calcular o dom\u00ednio de fun\u00e7\u00f5es radicais ou irracionais e, al\u00e9m disso, poder\u00e1 ver como represent\u00e1-las em um gr\u00e1fico com exemplos e praticar com exerc\u00edcios e problemas resolvidos passo &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/pt\/funcao-irracional-ou-radical\/\"> <span class=\"screen-reader-text\">Fun\u00e7\u00e3o irracional ou fun\u00e7\u00e3o radical<\/span> Leia mais &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"","footnotes":""},"categories":[22],"tags":[],"class_list":["post-8","post","type-post","status-publish","format-standard","hentry","category-representacao-de-funcao"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.2 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Fun\u00e7\u00e3o irracional ou fun\u00e7\u00e3o radical -<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathority.org\/pt\/funcao-irracional-ou-radical\/\" \/>\n<meta property=\"og:locale\" content=\"pt_BR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Fun\u00e7\u00e3o irracional ou fun\u00e7\u00e3o radical -\" \/>\n<meta property=\"og:description\" content=\"Esta p\u00e1gina explica o que \u00e9 uma fun\u00e7\u00e3o irracional, tamb\u00e9m chamada de fun\u00e7\u00e3o radical, bem como todas as caracter\u00edsticas deste tipo de fun\u00e7\u00e3o. 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