We can find the inverse function writing f(x) as y in the original function and then changing x with y and isolating y again, so
[tex]y=\sqrt[]{x}-5[/tex]
Changing y with x we have
[tex]x=\sqrt[]{y}-5[/tex]
Now we must get y on one side of the equation again, then
[tex]\begin{gathered} x=\sqrt[]{y}-5 \\ x+5=\sqrt[]{y} \\ (\sqrt[]{y})^2=(x+5)^2 \\ y=(x+5)^2 \end{gathered}[/tex]
The domain of the inverse function in the image of the original function f, the image of f is x ≥ -5, then the domain of the inverse of will be x ≥ -5, so our answer is
[tex]f^{-1}(x)=(x+5)^2,x\ge-5[/tex]
