Let y=f(x):
[tex]\begin{gathered} y=f(x) \\ \Rightarrow y=\sqrt[]{x}-6 \end{gathered}[/tex]
Isolate x from the equation:
[tex]\begin{gathered} \sqrt[]{x}=y+6 \\ \Rightarrow x=(y+6)^2 \end{gathered}[/tex]
Swap x and y:
[tex]\Rightarrow y=(x+6)^2[/tex]
Which is the inverse function of f(x).
Therefore:
[tex]y=(x+6)^2[/tex]
