## Calculus: Early Transcendentals (2nd Edition)

$f(x)=x^{4}+4$ $f^{-1}(x)=\sqrt[4]{x-4}$
$f(x)=x^{4}+4$, for $x\ge0$ Substitute $f(x)$ by $y$: $y=x^{4}+4$ Solve the equation for $x$. Start by taking $4$ to the left side: $y-4=x^{4}$ Take the fourth root of both sides and rearrange the equation: $\sqrt[4]{y-4}=\sqrt[4]{x^{4}}$ $x=\sqrt[4]{y-4}$ Interchange $x$ and $y$: $y=\sqrt[4]{x-4}$ Substitute $y$ by $f^{-1}(x)$: $f^{-1}(x)=\sqrt[4]{x-4}$ The graph of both the original function and its inverse is shown in the answer section.