let's recall that to find the inverse of any expression, we start off by doing a quick switcheroo on the variables, and then solve for "y".
[tex]\bf y = x^2-1\implies \stackrel{switcheroo}{x=y^2-1}\implies x+1=y^2\implies \sqrt{x+1}=\stackrel{f^{-1}(x)}{y}[/tex]