Chapter 9 - Section 9.2 - Inverse Functions - Exercise Set - Page 551: 35

$f^{-1}(x)=x^{3}$

$f(x)=\sqrt[3]{x}$ Substitute $f(x)$ by $y$ $y=\sqrt[3]{x}$ Solve for $x$ by raising both sides to the cubic power: $y^{3}=(\sqrt[3]{x})^{3}$ $y^{3}=x$ $x=y^{3}$ Interchange $x$ and $y$: $y=x^{3}$ Substitute $y$ by $f^{-1}(x)$ $f^{-1}(x)=x^{3}$