## Calculus 8th Edition

Published by Cengage

# Chapter 6 - Inverse Functions - 6.3 Logarithmic Functions - 6.3 Exercises: 61

#### Answer

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

#### 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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