Let’s first look at the given functions:<\/p>\n\n\n\n
- \n
- f(x)=x+5×2+4x3f(x) = x + 5x^2 + 4x^3f(x)=x+5×2+4×3<\/li>\n\n\n\n
- g(x)=x\u2212x25g(x) = x – \\frac{x^2}{5}g(x)=x\u22125×2\u200b<\/li>\n<\/ul>\n\n\n\n
Now, we need to find:<\/p>\n\n\n\n
- \n
- f(1x)f(1x)f(1x)<\/strong> \u2014 This represents substituting xxx with 1x1x1x, or just xxx, in the function f(x)f(x)f(x). f(1x)=f(x)=x+5×2+4x3f(1x) = f(x) = x + 5x^2 + 4x^3f(1x)=f(x)=x+5×2+4×3 Since f(x)f(x)f(x) is already expressed in terms of xxx, the result for f(1x)f(1x)f(1x) is simply: f(1x)=x+5×2+4x3f(1x) = x + 5x^2 + 4x^3f(1x)=x+5×2+4×3<\/li>\n\n\n\n
- g(\u2212x2)g(-x^2)g(\u2212x2)<\/strong> \u2014 This represents substituting xxx with \u2212x2-x^2\u2212x2 in the function g(x)g(x)g(x). g(\u2212x2)=\u2212x2\u2212(\u2212x2)25g(-x^2) = -x^2 – \\frac{(-x^2)^2}{5}g(\u2212x2)=\u2212x2\u22125(\u2212x2)2\u200b Simplifying the expression: g(\u2212x2)=\u2212x2\u2212x45g(-x^2) = -x^2 – \\frac{x^4}{5}g(\u2212x2)=\u2212x2\u22125×4\u200b<\/li>\n<\/ol>\n\n\n\n
So, the final answers are:<\/p>\n\n\n\n
- \n
- f(1x)=x+5×2+4x3f(1x) = x + 5x^2 + 4x^3f(1x)=x+5×2+4×3<\/li>\n\n\n\n
- g(\u2212x2)=\u2212x2\u2212x45g(-x^2) = -x^2 – \\frac{x^4}{5}g(\u2212x2)=\u2212x2\u22125×4\u200b<\/li>\n<\/ol>\n\n\n\n
Explanation:<\/h3>\n\n\n\n
For f(1x)f(1x)f(1x), since there is no transformation needed other than replacing xxx with 1x1x1x, the function stays the same. The expression f(x)=x+5×2+4x3f(x) = x + 5x^2 + 4x^3f(x)=x+5×2+4×3 remains unchanged when we evaluate f(1x)f(1x)f(1x).<\/p>\n\n\n\n
For g(\u2212x2)g(-x^2)g(\u2212x2), we substitute \u2212x2-x^2\u2212x2 into the expression for g(x)g(x)g(x). After substituting, we have to simplify the terms. The square of \u2212x2-x^2\u2212x2 is just x4x^4×4, so the final result is \u2212x2\u2212x45-x^2 – \\frac{x^4}{5}\u2212x2\u22125×4\u200b.<\/p>\n\n\n\n
![\"\"](\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner9-261.jpeg\")
<\/figure>\n","protected":false},"excerpt":{"rendered":"The functions f and g are defined as follows. =fx+5×2+4×3 and =gx\u2212x25x Find f1x and g\u2212x2 . Write your answers without parentheses and simplify them as much as possible. The Correct Answer and Explanation is: Let’s first look at the given functions: Now, we need to find: So, the final answers are: Explanation: For f(1x)f(1x)f(1x), […]<\/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-258889","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/258889","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=258889"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/258889\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=258889"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=258889"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=258889"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
- g(\u2212x2)g(-x^2)g(\u2212x2)<\/strong> \u2014 This represents substituting xxx with \u2212x2-x^2\u2212x2 in the function g(x)g(x)g(x). g(\u2212x2)=\u2212x2\u2212(\u2212x2)25g(-x^2) = -x^2 – \\frac{(-x^2)^2}{5}g(\u2212x2)=\u2212x2\u22125(\u2212x2)2\u200b Simplifying the expression: g(\u2212x2)=\u2212x2\u2212x45g(-x^2) = -x^2 – \\frac{x^4}{5}g(\u2212x2)=\u2212x2\u22125×4\u200b<\/li>\n<\/ol>\n\n\n\n
- f(1x)f(1x)f(1x)<\/strong> \u2014 This represents substituting xxx with 1x1x1x, or just xxx, in the function f(x)f(x)f(x). f(1x)=f(x)=x+5×2+4x3f(1x) = f(x) = x + 5x^2 + 4x^3f(1x)=f(x)=x+5×2+4×3 Since f(x)f(x)f(x) is already expressed in terms of xxx, the result for f(1x)f(1x)f(1x) is simply: f(1x)=x+5×2+4x3f(1x) = x + 5x^2 + 4x^3f(1x)=x+5×2+4×3<\/li>\n\n\n\n