Answer
$ f^{-1}(x)=x^{3}-2$
Work Step by Step
We are given the function, $f(x)=\sqrt[3] (x+2)$. First, we must replace $f(x)$ with y.
$y=\sqrt[3] (x+2)$
Next, interchange x and y.
$x=\sqrt[3] (y+2)$
Next, cube both sides.
$x^{3}=(\sqrt[3] (y+2))^{3}$
$x^{3}=y+2$
Next, subtract 2 from both sides.
$y=x^{3}-2$
Finally, replace y with $f^{-1}(x)$.
$ f^{-1}(x)=x^{3}-2$
