Given:
f(x) = root x - 5
Rewrite the function using y,
[tex]y=\sqrt[]{x}-5[/tex]Now, interchange the position of x and y in the function,
[tex]x=\sqrt[]{y}-5[/tex]Isolate the dependent variable
[tex]\begin{gathered} \sqrt[]{y}=x+5 \\ y=(x+5)^2 \end{gathered}[/tex]Therefore,
[tex]f^{-1}(x)=(x+5)^2[/tex]And the domain is minus infinity to infinity
[tex]\begin{gathered} f^{-1}(x)=(x+5)^2 \\ \text{Domain}=(-\infty,\infty) \end{gathered}[/tex]