Answer
$f(x)=\sqrt{x}$
$f^{-1}(x)=x^{2}$
Work Step by Step
$f(x)=\sqrt{x}$, for $x\ge0$
Substitute $f(x)$ by $y$:
$y=\sqrt{x}$
Solve the equation for $x$. Do so by squaring both sides and rearranging the equation:
$y^{2}=(\sqrt{x})^{2}$
$x=y^{2}$
Interchange $x$ and $y$:
$y=x^{2}$
Substitute $y$ by $f^{-1}(x)$:
$f^{-1}(x)=x^{2}$
The graph of both the original function and its inverse is shown in the answer section.
