Answer
$f^{-1}(x)=x^{3}-1$
Work Step by Step
$f(x)=\sqrt[3]{x+1}$
Replace $f(x)$ with $y$:
$y=\sqrt[3]{x+1}$
Interchange $x$ and $y$:
$x=\sqrt[3]{y+1}$
Let's solve for $y$. Start by cubing both sides:
$x^{3}=(\sqrt[3]{y+1})^{3}$
$x^{3}=y+1$
Take the $1$ to the left side:
$x^{3}-1=y$
Replace $y$ with $f^{-1}(x)$:
$f^{-1}(x)=x^{3}-1$
