#### Answer

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

#### Work Step by Step

We are given:
$f(x)=(x+1)^{3}$
To find the inverse function, we switch $x$ and $y$ and solve for $y$:
$y=(x+1)^{3}$
$x=(y+1)^{3}$
$\sqrt[3]{x}=y+1$
$\sqrt[3]{x}-1=y$
Thus the inverse is:
$f^{-1}(x)=\sqrt[3]{x}-1$