{"id":152968,"date":"2024-10-12T09:31:25","date_gmt":"2024-10-12T09:31:25","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=152968"},"modified":"2024-10-12T09:31:28","modified_gmt":"2024-10-12T09:31:28","slug":"find-the-function-inverse-f-1x-of-y-2x-1","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/10\/12\/find-the-function-inverse-f-1x-of-y-2x-1\/","title":{"rendered":"Find the function inverse ,f-1(x) , of y = 2x + 1."},"content":{"rendered":"\n<p>Find the function inverse ,f-1(x) , of y = 2x + 1.<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To find the inverse function ( f^{-1}(x) ) of the function ( y = f(x) = 2x + 1 ), follow these steps:<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Replace ( f(x) ) with ( y )<\/h3>\n\n\n\n<p>Start by rewriting the function in terms of ( y ):<br>[<br>y = 2x + 1<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Solve for ( x )<\/h3>\n\n\n\n<p>To find the inverse, we need to express ( x ) in terms of ( y ). Start by isolating ( x ):<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Subtract 1 from both sides:<br>[<br>y &#8211; 1 = 2x<br>]<\/li>\n\n\n\n<li>Divide both sides by 2:<br>[<br>x = \\frac{y &#8211; 1}{2}<br>]<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Switch ( x ) and ( y )<\/h3>\n\n\n\n<p>Since we are looking for the inverse function, we replace ( y ) with ( x ):<br>[<br>f^{-1}(x) = \\frac{x &#8211; 1}{2}<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Conclusion<\/h3>\n\n\n\n<p>Thus, the inverse function is:<br>[<br>f^{-1}(x) = \\frac{x &#8211; 1}{2}<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation of the Process<\/h3>\n\n\n\n<p>Finding the inverse of a function essentially involves reversing the roles of the input and output. The original function ( y = 2x + 1 ) transforms ( x ) values into ( y ) values through a linear relationship. To derive the inverse, we start by expressing the function as an equation in ( y ) and then isolate ( x ) to express it in terms of ( y ).<\/p>\n\n\n\n<p>By rearranging the equation, we find ( x ) as a function of ( y ). In this case, we subtracted 1 from both sides to eliminate the constant term on the right side and then divided by 2 to isolate ( x ). The crucial step is to remember to switch ( x ) and ( y ) once we have isolated ( x ).<\/p>\n\n\n\n<p>The resulting inverse function ( f^{-1}(x) = \\frac{x &#8211; 1}{2} ) indicates that for any ( x ) value, we can find the original input of the function ( f(x) ) by first subtracting 1 and then dividing the result by 2. This method can be applied to any one-to-one function, ensuring that each output corresponds to exactly one input, allowing for the proper definition of an inverse function.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Find the function inverse ,f-1(x) , of y = 2x + 1. The Correct Answer and Explanation is: To find the inverse function ( f^{-1}(x) ) of the function ( y = f(x) = 2x + 1 ), follow these steps: Step 1: Replace ( f(x) ) with ( y ) Start by rewriting the [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","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":"","ast-disable-related-posts":"","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":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-152968","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/152968","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=152968"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/152968\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=152968"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=152968"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=152968"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}