Calculus, 10th Edition (Anton)

Published by Wiley
ISBN 10: 0-47064-772-8
ISBN 13: 978-0-47064-772-1

Chapter 0 - Before Calculus - 0.4 Inverse Functions - Exercises Set 0.4 - Page 45: 12


The answer is $f^{-1}(x)=\frac{x^{5}-2}{4}\\$

Work Step by Step

$\ The\ given\ function\ is\ f(x)=\sqrt[5]{4x+2}\\ \ This\ can\ be\ rewritten\ as\ y=\sqrt[5]{4x+2}\\ \ Taking\ the\ fifth\ power\ on\ both\ sides\ we\ get\ ,\\ y^{5}=4x+2\\ \ Subtracting\ 2\ on\ both\ sides\ we\ get\ ,\\ 4x=y^{5}-2\\ \ Dividing\ on\ both\ sides\ by\ 4\ we\ get\ ,\\ x=\frac{y^{5}-2}{4}\\ \ So\ we\ get\ f^{-1}(x)=\frac{x^{5}-2}{4}\\$
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