{"id":11,"date":"2023-09-17T11:15:57","date_gmt":"2023-09-17T11:15:57","guid":{"rendered":"https:\/\/mathority.org\/it\/funzione-irrazionale-o-radicale\/"},"modified":"2023-09-17T11:15:57","modified_gmt":"2023-09-17T11:15:57","slug":"funzione-irrazionale-o-radicale","status":"publish","type":"post","link":"https:\/\/mathority.org\/it\/funzione-irrazionale-o-radicale\/","title":{"rendered":"Funzione irrazionale o funzione radicale"},"content":{"rendered":"<p>Questa pagina spiega cos&#8217;\u00e8 una funzione irrazionale, detta anche funzione radicale, e tutte le caratteristiche di questo tipo di funzione. Scoprirai anche come calcolare il dominio delle funzioni radicali o irrazionali e, inoltre, potrai vedere come rappresentarle su un grafico con esempi ed esercitarti con esercizi e problemi risolti passo dopo passo. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-una-funcion-irracional-o-radical\"><\/span> Cos&#8217;\u00e8 una funzione irrazionale (o radicale)?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Una funzione irrazionale ha lo stesso significato di una funzione radicale e, pertanto, condividono una definizione: <\/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\"> Una <strong>funzione irrazionale<\/strong> , detta anche <strong>funzione radicale<\/strong> , \u00e8 una funzione che ha la variabile indipendente x sotto il simbolo di una radice.<\/p>\n<\/div>\n<p> Come gi\u00e0 sappiamo, il risultato di una radice pu\u00f2 essere positivo o negativo. Quindi la rappresentazione di una funzione irrazionale (o radicale) ha due possibili curve: <\/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=\"esempi di funzioni irrazionali o radicali\" class=\"wp-image-177\" width=\"430\" height=\"366\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p> Ma se il segno non \u00e8 specificato, si suppone che sia rappresentata la funzione positiva.<\/p>\n<p> D\u2019altra parte, una funzione irrazionale non deve essere confusa con una funzione razionale. Sebbene abbiano nomi molto simili, si tratta di due tipi di funzioni completamente diverse. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"dominio-de-una-funcion-irracional-o-radical\"><\/span> Dominio di una funzione irrazionale o radicale<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Il dominio di una funzione con radici dipende dalla parit\u00e0 dell&#8217;indice radice, cio\u00e8 dipende dal fatto che l&#8217;indice radicale sia pari o dispari. <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"dominio-de-una-funcion-con-raiz-de-indice-par\"><\/span> Dominio di una funzione con radice di indice pari<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> Come ben sai, non esiste la radice (neppure l&#8217;indice) di un numero negativo. Pertanto, <strong>una funzione radicale con indice pari esister\u00e0 finch\u00e9 il suo contenuto sar\u00e0 uguale o maggiore di 0.<\/strong><\/p>\n<p> Ad esempio, vediamo come viene calcolato il dominio della seguente funzione radicale o irrazionale:<\/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> Questa \u00e8 una funzione di indice radicale pari, quindi dobbiamo guardare quando il suo contenuto \u00e8 positivo o 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> Risolviamo la disuguaglianza:<\/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> Quindi la funzione esister\u00e0 ogni volta che x \u00e8 maggiore o uguale a 4 ed \u00e8 indicata dal seguente intervallo: <\/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> Dominio di una funzione con radice di indice dispari<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> Le funzioni irrazionali con indice dispari non presentano questo problema, poich\u00e9 esiste la radice dell&#8217;indice dispari di un numero 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> Pertanto, esistono funzioni radicali di indice dispari per qualsiasi valore di <em>x<\/em> . Ovvero, in altre parole, <strong>il dominio \u00e8 formato solo da numeri reali<\/strong> .<\/p>\n<p> Ad esempio, calcoleremo il dominio di definizione della seguente funzione radicale il cui indice \u00e8 dispari:<\/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> Poich\u00e9 \u00e8 una funzione irrazionale con indice dispari, il suo dominio \u00e8 costituito da numeri reali: <\/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> Come rappresentare una funzione irrazionale o radicale<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Vediamo come rappresentare una funzione con radici su un grafico utilizzando un esempio.<\/p>\n<ul>\n<li> Traccia su un grafico la seguente funzione radicale o irrazionale:<\/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> La prima cosa da fare \u00e8 trovare il dominio della funzione. Poich\u00e9 \u00e8 una radice quadrata, tutto ci\u00f2 che contiene deve essere positivo, poich\u00e9 non esiste una radice quadrata di un numero negativo. Pertanto, la funzione radicale esister\u00e0 finch\u00e9 il suo contenuto sar\u00e0 uguale o maggiore di 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> Pertanto, il dominio della funzione \u00e8 costituito da tutti i numeri maggiori o uguali a -2. Questo \u00e8 da dire:<\/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> Una volta conosciuto il dominio della funzione, creiamo una tabella di valori. Ovviamente, pi\u00f9 punti calcoliamo, pi\u00f9 precisa sar\u00e0 la rappresentazione della funzione. Ma \u00e8 sufficiente calcolare 3 o 4 punti nell&#8217;intervallo del dominio: <\/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> Rappresentiamo ora i punti ottenuti su un grafico <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=\"come rappresentare una funzione radicale o irrazionale\" class=\"wp-image-178\" width=\"460\" height=\"249\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p> Infine uniamo i punti ed estendiamo la curva per indicare che la funzione continua a crescere: <\/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=\"esempio di rappresentazione grafica di una funzione radicale o irrazionale\" 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>Esercizi risolti su funzioni irrazionali o radicali<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3 class=\"wp-block-heading\"> Esercizio 1<\/h3>\n<p> Trova il dominio della seguente funzione radicale: <\/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>Vedi la soluzione<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> La radice quadrata di un numero negativo non esiste. Pertanto, la funzione esister\u00e0 quando l&#8217;argomento radice \u00e8 positivo o 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\">Esercizio 2<\/h3>\n<p> Trova il dominio della seguente funzione irrazionale: <\/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>Vedi la soluzione<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> La radice quadrata di un numero negativo non ha soluzione reale. Pertanto, la funzione esister\u00e0 finch\u00e9 il contenuto della radice sar\u00e0 positivo o 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\"> Ricorda che se in una disuguaglianza cambiamo i lati di un numero negativo che moltiplica o divide, dobbiamo ruotare anche il segno della disuguaglianza. <\/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\">Esercizio 3<\/h3>\n<p> Traccia su un grafico la seguente funzione irrazionale: <\/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>Vedi la soluzione<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Innanzitutto dobbiamo calcolare il dominio della funzione: <\/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\"> Ora creiamo un array di valori fornendo i valori della funzione nell&#8217;intervallo di dominio: <\/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\"> Infine tracciamo i punti e tracciamo la funzione sul grafico: <\/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=\"esercizio risolto passo dopo passo di una funzione irrazionale o radicale\" 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\"> Esercizio 4<\/h3>\n<p> Rappresentare graficamente la seguente funzione irrazionale o radicale: <\/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>Vedi la soluzione<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Innanzitutto dobbiamo calcolare il dominio della funzione: <\/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\"> Ora creiamo un array di valori fornendo i valori della funzione nell&#8217;intervallo di dominio: <\/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\"> Infine tracciamo i punti e disegniamo la funzione sul grafico: <\/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=\"esercizio risolto passo dopo passo di una funzione irrazionale o radicale\" 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\"> Esercizio 5<\/h3>\n<p> Rappresentare graficamente la seguente funzione irrazionale o radicale: <\/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>Vedi la soluzione<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Prima di tracciare la funzione, dobbiamo calcolare il dominio della funzione: <\/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\"> Ricorda che se in una disuguaglianza cambiamo i lati di un numero negativo che moltiplica o divide, dobbiamo cambiare anche il segno della disuguaglianza. <\/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\"> Ora costruiamo una tabella di valori valutando la funzione nei punti che appartengono al dominio della funzione: <\/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 infine, rappresenta semplicemente i punti e dipingi la funzione sul grafico: <\/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=\"determinati esercizi di funzioni radicali o irrazionali\" 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\"> Esercizio 6<\/h3>\n<p> Traccia la seguente funzione irrazionale o radicale su un grafico: <\/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>Vedi la soluzione<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Dobbiamo prima calcolare il dominio della funzione:<\/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\"> In questo caso, abbiamo ottenuto una disuguaglianza di secondo grado, quindi dobbiamo applicare la formula delle equazioni quadratiche per risolverla: <\/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\"> Dividiamo la linea in tre pezzi con le radici ottenute: <\/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 sostituiamo un numero per ciascuna sezione della disuguaglianza, per vedere quali sezioni soddisfano la disuguaglianza e, quindi, appartengono al dominio:<\/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\"> Pertanto, le sezioni che rispettano la disuguaglianza sono quelle dei lati: <\/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\"> Il dominio della funzione \u00e8 quindi:<\/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\"> Una volta calcolato il dominio della funzione, costruiamo una tabella di valori che riporta i valori della funzione nell&#8217;intervallo del dominio: <\/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\"> Infine, rappresentiamo i punti ottenuti sul grafico e tracciamo la funzione: <\/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=\"grafico di una funzione irrazionale o radicale con indice pari\" 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\"> Esercizio 7<\/h3>\n<p> Rappresentate sul grafico la seguente funzione formata da una radice: <\/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>Vedi la soluzione<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> \u00c8 una funzione irrazionale la cui radice ha un indice dispari, quindi il dominio della funzione \u00e8 costituito da numeri reali:<\/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\"> Possiamo quindi prendere qualsiasi punto per creare la tabella dei valori. In questo caso cercheremo molti punti perch\u00e9 \u00e8 una radice cubica: <\/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\"> Infine, tracciamo i punti trovati e tracciamo la funzione sul grafico: <\/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=\"rappresentare graficamente una funzione irrazionale o radicale con un indice dispari\" 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\"> Esercizio 8<\/h3>\n<p> Risolvi il seguente problema relativo alle funzioni irrazionali (o radicali):<\/p>\n<p> Il consumo della batteria di un cellulare \u00e8 dato dalla seguente funzione:<\/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> Dove il consumo \u00e8 espresso in milliampere (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> \u00e8 il tempo trascorso in minuti.<\/p>\n<p> Determinare il valore della costante<\/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> in modo che dopo 4 minuti il consumo sia di 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>Vedi la soluzione<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Che dopo 4 minuti il consumo sia 35 mA significa che quando t \u00e8 4, f(t) \u00e8 35. Quindi 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\"> Ora dobbiamo risolvere l&#8217;equazione che abbiamo ottenuto. Se guardi da vicino, \u00e8 un&#8217;equazione irrazionale poich\u00e9 ha una radice. In questo tipo di equazioni la prima cosa da fare \u00e8 isolare la radice di un membro, che in questo caso \u00e8 gi\u00e0 isolata. Una volta isolato, dobbiamo elevare al quadrato entrambi i lati dell&#8217;equazione:<\/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\"> Quindi semplifichiamo la radice:<\/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 risolviamo l&#8217;equazione: <\/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\"> Infine, nelle equazioni irrazionali, le soluzioni devono essere verificate. Dobbiamo quindi sostituire K=-1221 nell&#8217;equazione all&#8217;inizio: <\/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\"> Poich\u00e9 l&#8217;uguaglianza \u00e8 soddisfatta, K=-1221 \u00e8 una soluzione.<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Questa pagina spiega cos&#8217;\u00e8 una funzione irrazionale, detta anche funzione radicale, e tutte le caratteristiche di questo tipo di funzione. Scoprirai anche come calcolare il dominio delle funzioni radicali o irrazionali e, inoltre, potrai vedere come rappresentarle su un grafico con esempi ed esercitarti con esercizi e problemi risolti passo dopo passo. Cos&#8217;\u00e8 una funzione &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/it\/funzione-irrazionale-o-radicale\/\"> <span class=\"screen-reader-text\">Funzione irrazionale o funzione radicale<\/span> Leggi altro &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":[17],"tags":[],"class_list":["post-11","post","type-post","status-publish","format-standard","hentry","category-rappresentazione-delle-funzioni"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.2 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Funzione irrazionale o funzione radicale -<\/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\/it\/funzione-irrazionale-o-radicale\/\" \/>\n<meta property=\"og:locale\" content=\"it_IT\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Funzione irrazionale o funzione radicale -\" \/>\n<meta property=\"og:description\" content=\"Questa pagina spiega cos&#8217;\u00e8 una funzione irrazionale, detta anche funzione radicale, e tutte le caratteristiche di questo tipo di funzione. 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