The function is not injective, therefore the inverse doesn't exist.
[tex]For\ x\geq0[/tex]
[tex] f(x)=x^2-16\\\\f^{-1}(x)=?\\\\y=x^2-16\to x=y^2-16\ \ \ \ |+16\\\\x+16=y^2\\\\y^2=x+16\to y=\sqrt{x+16}\ for\ x\geq-16 [/tex]
