{"id":156326,"date":"2022-03-26T01:37:57","date_gmt":"2022-03-25T20:07:57","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/inverse-functions-definition-types-and-examples-with-solution\/"},"modified":"2025-02-11T10:46:59","modified_gmt":"2025-02-11T05:16:59","slug":"inverse-functions-definition-types-and-examples-with-solution","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/maths\/inverse-functions\/","title":{"rendered":"Inverse Functions \u2013 Definition, Types and Examples with Solution"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_37 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" style=\"display: none;\"><label for=\"item\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/label><input type=\"checkbox\" id=\"item\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1' style='display:block'><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/inverse-functions\/#Inverse_Functions\" title=\"Inverse Functions\">Inverse Functions<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/inverse-functions\/#Example_1_Find_the_Inverse_Function\" title=\"Example 1)  Find the Inverse Function\">Example 1)  Find the Inverse Function<\/a><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"Inverse_Functions\"><\/span>Inverse Functions<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p dir=\"ltr\">A function<\/a> starts with a value then performs some operation on it and the created output leads to the answer. The inverse function starts with the output answer then performs some operation on it and brings us back to the starting value. An inverse function basically interchanges the first and second elements of each pair of the original function. Inverse Functions \u2013 Definition Types and Examples with Solution.<\/p>\n<p dir=\"ltr\">For example, consider that a graph of a function has (a and b) as its points, the graph of an inverse function will have the points (b and a ). An inverse function is written as f<span id=\"MathJax-Element-1-Frame\" class=\"MathJax\" style=\"box-sizing: border-box; font-family: 'Open Sans', sans-serif; -webkit-tap-highlight-color: rgba(255, 255, 255, 0); display: inline; font-style: normal; font-weight: normal; line-height: 49px; font-size: 17.3333px; text-indent: 0px; text-align: center; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;\" tabindex=\"0\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot; display=&quot;block&quot;&gt;&lt;msup&gt;&lt;mi&gt;&lt;\/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mo&gt;&amp;#x2212;&lt;\/mo&gt;&lt;mn&gt;1&lt;\/mn&gt;&lt;\/mrow&gt;&lt;\/msup&gt;&lt;\/math&gt;\"><span id=\"MathJax-Span-1\" class=\"math\"><span id=\"MathJax-Span-2\" class=\"mrow\"><span id=\"MathJax-Span-3\" class=\"msubsup\"><span id=\"MathJax-Span-4\" class=\"mi\"><\/span><span id=\"MathJax-Span-5\" class=\"texatom\"><span id=\"MathJax-Span-6\" class=\"mrow\"><span id=\"MathJax-Span-7\" class=\"mo\">\u2212<\/span><span id=\"MathJax-Span-8\" class=\"mn\">1<\/span><\/span><\/span><\/span><\/span><\/span><\/span>(x)<\/p>\n<p dir=\"ltr\">Let us take another example, consider f(x) = 3x \u2013 6. What happens to x? We first multiply by 3 and then subtract 6 from the result. But in the reverse function, we follow the steps backward by first adding 6 to undo the subtraction and then divide it by 3 to undo the multiplication.<\/p>\n<p dir=\"ltr\"><img loading=\"lazy\" class=\"aligncenter wp-image-156325 size-full\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/inverse-functions-definition-types-and-examples-with-solution.jpg\" alt=\"Inverse Functions \u2013 Definition, Types and Examples with Solution\" width=\"606\" height=\"428\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/inverse-functions-definition-types-and-examples-with-solution.jpg?v=1648238875 606w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/inverse-functions-definition-types-and-examples-with-solution-300x212.jpg?v=1648238875 300w\" sizes=\"(max-width: 606px) 100vw, 606px\" \/><\/p>\n<p dir=\"ltr\">How to find the Inverse of a Function<\/p>\n<p dir=\"ltr\">Since we now know what an inverse function is, wouldn\u2019t you want to know how to solve inverse functions? What are we waiting for then? Let\u2019s unwrap the mystery.<\/p>\n<p dir=\"ltr\">There are three methods to find the inverse of a function.<\/p>\n<ol>\n<li dir=\"ltr\">\n<p dir=\"ltr\" role=\"presentation\">Simply swapping the ordered pairs<\/p>\n<\/li>\n<li dir=\"ltr\">\n<p dir=\"ltr\" role=\"presentation\">Solve it algebraically<\/p>\n<\/li>\n<li dir=\"ltr\">\n<p dir=\"ltr\" role=\"presentation\">Using A graph<\/p>\n<\/li>\n<\/ol>\n<h2>Example 1)  Find the Inverse Function<\/h2>\n<p>The <a href=\"https:\/\/en.wikipedia.org\/wiki\/Inverse_function\" target=\"_blank\" rel=\"noopener\">inverse function<\/a> of is .<\/p>\n<p>To find the inverse function, we must first determine its function&#8217;s inverse relation. We do this by solving for y in terms of x.<\/p>\n<p>Next, we must determine the function&#8217;s inverse function&#8217;s domain and range.<\/p>\n<p>The inverse function&#8217;s domain is the set of all x-values for which the function&#8217;s original relation is true. The inverse function&#8217;s range is the set of all y-values for which the inverse function is also true.<\/p>\n<p>In this example, the inverse function&#8217;s domain is all real numbers except for x = 2 and the inverse function&#8217;s range is all real numbers except for y = 1.<\/p>\n<p>Inverse Functions \u2013 Definition Types and Examples with Solution.<\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Inverse Functions A function starts with a value then performs some operation on it and the created output leads to [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"Inverse Functions \u2013 Definition Types and Examples with Solution","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"Learn about Inverse Functions \u2013 Definition Types and Examples with Solution by subject experts on infinitylearn.com.","custom_permalink":"maths\/inverse-functions\/"},"categories":[13],"tags":[],"table_tags":[],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.9 - 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