Manipulating Radical Functions

To find the inverse of $f(x),$ we first need to replace $f(x)$ with $y.$ $$\begin{array}{c}f(x)=\text{-}\sqrt{x}\to y=\text{-}\sqrt{x}\end{array}$$ Next step is to switch $x$ and $y$ in the function rule. $$y=\text{-}\sqrt{x}\stackrel{\text{switch}}{\iff }x=\text{-}\sqrt{y}$$ Now we need to solve for $y.$ The resulting equation will be the inverse of the given function. Finally, to indicate that this is the inverse of $f(x),$ we will replace $y$ with $f^{\text{-}1}(x).$ $$\begin{array}{c}y=x^2\to f^{\text{-}1}(x)=x^2\end{array}$$