Chapter 9 - Section 9.2 - Inverse Functions - Exercise Set - Page 551: 29

$f^{-1}(x)=\sqrt[3]{x}$ The graph of both functions is shown below:

$f(x)=x^{3}$ Substitute $f(x)$ by $y$: $y=x^{3}$ Solve for $x$. Do so by taking the cubic root of both sides of the equation: $\sqrt[3]{x^{3}}=\sqrt[3]{y}$ $x=\sqrt[3]{y}$ Interchange $x$ and $y$: $y=\sqrt[3]{x}$ Substitute $y$ by $f^{-1}(x)$: $f^{-1}(x)=\sqrt[3]{x}$