Answer
$f^{-1}(x)=\sqrt[3]{x}-2$
Work Step by Step
$f(x)=(x+2)^{3}$
Replace $f(x)$ with $y$:
$y=(x+2)^{3}$
Interchange $x$ and $y$:
$x=(y+2)^{3}$
Solve for $y$. Begin by taking the cubic root of both sides:
$\sqrt[3]{x}=\sqrt[3]{(y+2)^{3}}$
$\sqrt[3]{x}=y+2$
Take the $2$ to the left side:
$\sqrt[3]{x}-2=y$
Replace $y$ with $f^{-1}(x)$:
$f^{-1}(x)=\sqrt[3]{x}-2$
