Swap the y with the x. So
[tex]y=x^2-12[/tex]
[tex]x = y^2-12[/tex]
Now solve for y
[tex]x = y^2-12[/tex]
[tex]x + 12 = y^2[/tex]
[tex]\sqrt{x + 12} = \sqrt{y^2}[/tex]
[tex]\sqrt{x + 12} = y[/tex]
[tex]y = \sqrt{x + 12}[/tex]
Inverse notation:
[tex]f(x)^{-1} = \sqrt{x + 12}[/tex]
