when getting the "inverse relation" of any expression, you'd always start off by doing a quick switcharoo on the variables, and then solve for "y", let's do so.
[tex]\bf \stackrel{f(x)}{y}=x^2-6\qquad inverse\implies \boxed{x}=\boxed{y}^2-6
\\\\\\
x+6=y^2\implies \sqrt{x+6}=\stackrel{f^{-1}(x)}{y}[/tex]
