Answer:[tex]f^{-1}=+-\sqrt{x+1}[/tex]Step-by-step explanation:f(x) = x^2 -1We need to find f^-1(x)WE find inverse of f(x)Replace f(x) with y[tex]y= x^2 -1[/tex]Replace x with y and y with x[tex]x= y^2 -1[/tex]Solve for yadd 1 on both sides , [tex]x+1= y^2[/tex]To remove square , take square root on both sides[tex]\sqrt{x+1} =\sqrt{y^2}[/tex][tex]\sqrt{x+1} =y[/tex][tex]y=+-\sqrt{x+1}[/tex]Replace y with f^-1[tex]f^{-1}=+-\sqrt{x+1}[/tex]