Answer
$ f^{-1}(x)=\sqrt[3] (x+5)$
Work Step by Step
We are given the function, $f(x)=x^{3}-5$. First, we must replace $f(x)$ with y.
$y=x^{3}-5$
Next, interchange x and y.
$x=y^{3}-5$
Next, solve for y by adding 5 to both sides.
$y^{3}=x+5$
Take the cube root of both sides.
$\sqrt[3] (y^{3})=y=\sqrt[3] (x+5)$
Finally, replace y with $f^{-1}(x)$.
$ f^{-1}(x)=\sqrt[3] (x+5)$
