Answer
$f(x)=x^{4}+4$
$f^{-1}(x)=\sqrt[4]{x-4}$
Work Step by Step
$f(x)=x^{4}+4$, 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.
