Manipulating Radical Functions

To find the inverse of $f(x),$ we first need to replace $f(x)$ with $y.$ $$\begin{array}{c}f(x)=\sqrt{\text{-}x+3}\to y=\sqrt{\text{-}x+3}\end{array}$$ Next step is to switch $x$ and $y$ in the function rule. $$y=\sqrt{\text{-}x+3}\stackrel{\text{switch}}{⟶}x=\sqrt{\text{-}y+3}$$ 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 $f^{\text{-}1}(x).$ $$\begin{array}{c}y=\text{-}{x}^2+3\to f^{\text{-}1}(x)=\text{-}{x}^2+3\end{array}$$