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