## Algebra: A Combined Approach (4th Edition)

$f^{-1}(x)=\sqrt[3]{x}+5$
$f(x)=(x-5)^{3}$ Replace $f(x)$ with $y$: $y=(x-5)^{3}$ Interchange $x$ and $y$: $x=(y-5)^{3}$ Solve for $y$. Start by taking the cubic root of both sides: $\sqrt[3]{x}=\sqrt[3]{(y-5)^{3}}$ $\sqrt[3]{x}=y-5$ Take the $-5$ to the left side: $\sqrt[3]{x}+5=y$ Replace $y$ with $f^{-1}(x)$: $f^{-1}(x)=\sqrt[3]{x}+5$