{"id":51,"date":"2023-09-17T11:15:57","date_gmt":"2023-09-17T11:15:57","guid":{"rendered":"https:\/\/mathority.org\/nl\/irrationele-of-radicale-functie\/"},"modified":"2023-09-17T11:15:57","modified_gmt":"2023-09-17T11:15:57","slug":"irrationele-of-radicale-functie","status":"publish","type":"post","link":"https:\/\/mathority.org\/nl\/irrationele-of-radicale-functie\/","title":{"rendered":"Irrationele functie of radicale functie"},"content":{"rendered":"<p>Op deze pagina wordt uitgelegd wat een irrationele functie, ook wel radicale functie genoemd, is, evenals alle kenmerken van dit type functie. Je ontdekt ook hoe je het domein van radicale of irrationele functies kunt berekenen en bovendien kun je zien hoe je ze in een grafiek met voorbeelden kunt weergeven en oefenen met oefeningen en problemen die stap voor stap worden opgelost. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-una-funcion-irracional-o-radical\"><\/span> Wat is een irrationele (of radicale) functie?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Een irrationele functie betekent hetzelfde als een radicale functie en daarom delen ze een definitie: <\/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\"> Een <strong>irrationele functie<\/strong> , ook wel <strong>radicale functie<\/strong> genoemd, is een functie met de onafhankelijke variabele x onder het symbool van een wortel.<\/p>\n<\/div>\n<p> Zoals we al weten, kan het resultaat van een wortel positief of negatief zijn. De weergave van een irrationele (of radicale) functie heeft dus twee mogelijke curven: <\/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=\"voorbeelden van irrationele of radicale functies\" class=\"wp-image-177\" width=\"430\" height=\"366\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p> Maar als het teken niet is gespecificeerd, wordt verondersteld dat de positieve functie wordt weergegeven.<\/p>\n<p> Aan de andere kant mag een irrationele functie niet worden verward met een rationele functie. Hoewel ze zeer vergelijkbare namen hebben, zijn het twee totaal verschillende soorten functies. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"dominio-de-una-funcion-irracional-o-radical\"><\/span> Domein van een irrationele of radicale functie<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Het domein van een functie met wortels hangt af van de pariteit van de wortelindex, dat wil zeggen, het hangt ervan af of de radicale index even of oneven is. <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"dominio-de-una-funcion-con-raiz-de-indice-par\"><\/span> Domein van een functie met wortel of even index<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> Zoals u wel weet, bestaat er geen wortel (zelfs index) van een negatief getal. Daarom <strong>zal een radicale functie met een even index bestaan zolang de inhoud gelijk is aan of groter is dan 0.<\/strong><\/p>\n<p> Laten we als voorbeeld eens kijken hoe het domein van de volgende radicale of irrationele functie wordt berekend:<\/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> Dit is een radicaal even indexfunctie, dus we moeten kijken wanneer de inhoud positief of nul is <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> We lossen de ongelijkheid op:<\/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> De functie zal dus bestaan wanneer x groter is dan of gelijk is aan 4, en wordt aangegeven door het volgende interval: <\/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> Domein van een functie met wortel van oneven index<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> Irrationele functies met oneven index hebben dit probleem niet, aangezien de oneven indexwortel van een negatief getal bestaat:<\/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> Daarom bestaan er radicale functies met een oneven index voor elke waarde van <em>x<\/em> . Of, met andere woorden, <strong>het domein bestaat alleen uit re\u00eble getallen<\/strong> .<\/p>\n<p> We zullen bijvoorbeeld het definitiedomein berekenen van de volgende radicale functie waarvan de index oneven is:<\/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> Omdat het een irrationele functie is met een oneven index, bestaat het domein uit re\u00eble getallen: <\/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> Hoe een irrationele of radicale functie weer te geven<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Laten we aan de hand van een voorbeeld kijken hoe we een functie met wortels in een grafiek kunnen weergeven.<\/p>\n<ul>\n<li> Teken de volgende radicale of irrationele functie in een grafiek:<\/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> Het eerste dat u moet doen, is het domein van de functie vinden. Omdat het een vierkantswortel is, moet alles wat erin staat positief zijn, aangezien er geen vierkantswortel is van een negatief getal. Daarom zal de radicale functie bestaan zolang de inhoud gelijk is aan of groter is dan 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> Het domein van de functie bestaat dus uit alle getallen groter dan of gelijk aan -2. Dat is te zeggen:<\/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> Zodra we het domein van de functie kennen, maken we een tabel met waarden. Het is duidelijk dat hoe meer punten we berekenen, hoe nauwkeuriger de weergave van de functie zal zijn. Maar het berekenen van 3 of 4 punten in het domeininterval is voldoende: <\/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> We geven nu de verkregen punten weer in een grafiek <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=\"hoe je een radicale of irrationele functie vertegenwoordigt\" class=\"wp-image-178\" width=\"460\" height=\"249\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p> En ten slotte voegen we de punten samen en verlengen we de curve om aan te geven dat de functie blijft groeien: <\/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=\"voorbeeld van een grafische weergave van een radicale of irrationele functie\" 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>Opgeloste oefeningen over irrationele of radicale functies<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3 class=\"wp-block-heading\"> Oefening 1<\/h3>\n<p> Zoek het domein van de volgende radicale functie: <\/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>Zie de oplossing<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> De vierkantswortel van een negatief getal bestaat niet. Daarom zal de functie bestaan als het hoofdargument positief of nul is: <\/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\">Oefening 2<\/h3>\n<p> Zoek het domein van de volgende irrationele functie: <\/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>Zie de oplossing<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> De vierkantswortel van een negatief getal heeft geen echte oplossing. Daarom zal de functie bestaan zolang de inhoud van de wortel positief of nul is: <\/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\"> Bedenk dat als we bij een ongelijkheid de zijden van een negatief getal dat vermenigvuldigt of deelt veranderen, we ook het teken van de ongelijkheid moeten roteren. <\/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\">Oefening 3<\/h3>\n<p> Teken de volgende irrationele functie in een grafiek: <\/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>Zie de oplossing<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Allereerst moeten we het domein van de functie berekenen: <\/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\"> Nu cre\u00ebren we een array van waarden door de waarden van de functie in het domeinbereik te geven: <\/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\"> Ten slotte plotten we de punten en plotten we de functie in de grafiek: <\/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=\"oefening stap voor stap opgelost van een irrationele of radicale functie\" 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\"> Oefening 4<\/h3>\n<p> Maak een grafiek van de volgende irrationele of radicaalfunctie: <\/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>Zie de oplossing<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Allereerst moeten we het domein van de functie berekenen: <\/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\"> Nu cre\u00ebren we een array van waarden door de waarden van de functie in het domeinbereik te geven: <\/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\"> Ten slotte plotten we de punten en tekenen we de functie in de grafiek: <\/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=\"oefening stap voor stap opgelost van een irrationele of radicale functie\" 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\"> Oefening 5<\/h3>\n<p> Maak een grafiek van de volgende irrationele of radicaalfunctie: <\/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>Zie de oplossing<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Voordat we de functie plotten, moeten we het domein van de functie berekenen: <\/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\"> Bedenk dat als we bij een ongelijkheid de zijden van een negatief getal dat vermenigvuldigt of deelt, veranderen, we ook het teken van de ongelijkheid moeten veranderen. <\/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\"> Nu construeren we een tabel met waarden door de functie te evalueren op punten die tot het domein van de functie behoren: <\/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\"> En tot slot, geef gewoon de punten weer en schilder de functie in de grafiek: <\/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=\"bepaalde oefeningen van radicale of irrationele functies\" 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\"> Oefening 6<\/h3>\n<p> Teken de volgende irrationele of radicale functie in een grafiek: <\/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>Zie de oplossing<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> We moeten eerst het domein van de functie berekenen:<\/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 dit geval hebben we een ongelijkheid van de tweede graad verkregen, dus moeten we de formule van de kwadratische vergelijkingen toepassen om deze op te lossen: <\/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\"> We verdelen de lijn in drie stukken met de verkregen wortels: <\/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\"> En we vervangen een getal voor elke sectie van de ongelijkheid, om te zien welke secties aan de ongelijkheid voldoen en daarom tot het domein behoren:<\/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\"> De secties die de ongelijkheid respecteren, zijn dus die van de zijkanten: <\/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\"> Het domein van de functie is daarom:<\/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\"> Nadat we het domein van de functie hebben berekend, construeren we een waardentabel met de waarden van de functie in het interval van het domein: <\/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\"> Ten slotte vertegenwoordigen we de verkregen punten in de grafiek en plotten we de functie: <\/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=\"grafiek van een irrationele of radicaalfunctie met even index\" 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\"> Oefening 7<\/h3>\n<p> Geef in de grafiek de volgende functie weer, gevormd door een wortel: <\/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>Zie de oplossing<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Het is een irrationele functie waarvan de wortel een oneven index heeft, dus het domein van de functie bestaat uit re\u00eble getallen:<\/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\"> We kunnen daarom elk punt gebruiken om de waardentabel te maken. In dit geval zullen we naar veel punten zoeken omdat het een derdemachtswortel is: <\/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\"> Ten slotte plotten we de gevonden punten en plotten we de functie in de grafiek: <\/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=\"grafiek van een irrationele of radicale functie met een oneven index\" 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\"> Oefening 8<\/h3>\n<p> Los het volgende probleem op dat verband houdt met irrationele (of radicale) functies:<\/p>\n<p> Het verbruik van de batterij van een mobiele telefoon wordt gegeven door de volgende functie:<\/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> Waarbij het verbruik wordt uitgedrukt in milliamp\u00e8re (mA) en<\/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> is de verstreken tijd in minuten.<\/p>\n<p> Bepaal de waarde van de 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> zodat na 4 minuten het verbruik 35 mA bedraagt. <\/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>Zie de oplossing<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Dat na 4 minuten het verbruik 35 mA is, betekent dat als t 4 is, f(t) 35 is. Dus 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\"> Nu moeten we de vergelijking die we hebben verkregen oplossen. Als je goed kijkt, is het een irrationele vergelijking, omdat het een wortel heeft. Bij dit soort vergelijkingen is het eerste wat je moet doen het isoleren van de wortel van \u00e9\u00e9n zijde, die in dit geval al ge\u00efsoleerd is. Eenmaal ge\u00efsoleerd, moeten we beide zijden van de vergelijking kwadrateren:<\/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\"> Vervolgens vereenvoudigen we de wortel:<\/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\"> En we lossen de vergelijking op: <\/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\"> Ten slotte moeten bij irrationele vergelijkingen de oplossingen worden geverifieerd. We moeten daarom K=-1221 in de vergelijking aan het begin vervangen: <\/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\"> Omdat aan de gelijkheid is voldaan, is K=-1221 een oplossing.<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Op deze pagina wordt uitgelegd wat een irrationele functie, ook wel radicale functie genoemd, is, evenals alle kenmerken van dit type functie. Je ontdekt ook hoe je het domein van radicale of irrationele functies kunt berekenen en bovendien kun je zien hoe je ze in een grafiek met voorbeelden kunt weergeven en oefenen met oefeningen &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/nl\/irrationele-of-radicale-functie\/\"> <span class=\"screen-reader-text\">Irrationele functie of radicale functie<\/span> Lees meer &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":[49],"tags":[],"class_list":["post-51","post","type-post","status-publish","format-standard","hentry","category-functie-representatie"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.2 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Irrationele functie of radicale functie -<\/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\/nl\/irrationele-of-radicale-functie\/\" \/>\n<meta property=\"og:locale\" content=\"nl_NL\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Irrationele functie of radicale functie -\" \/>\n<meta property=\"og:description\" content=\"Op deze pagina wordt uitgelegd wat een irrationele functie, ook wel radicale functie genoemd, is, evenals alle kenmerken van dit type functie. 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