Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 6 - Inverse Functions - 6.3* The Natural Exponential Function - 6.3* Exercises - Page 452: 25


$f^{-1}(x)=\sqrt[3] lnx$

Work Step by Step

Given: $f(x)=e^{x^{3}}$ Consider $y=e^{x^{3}}$ $lny=lne^{x^{3}}$ $lny=x^{3}$ Now, replace the terms to find out the value of inverse function. $lnx=y^{3}$ $y=\sqrt[3] lnx$ Hence, $f^{-1}(x)=\sqrt[3] lnx$
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