the assumption here is that the function f(x), has an inverse function of f⁻¹(x), so let's assume that is indeed the case, f⁻¹(x) is the inverse function of f(x).
for functions and their inverse, if they're indeed inverse of each other, then
f⁻¹( f(x) ) = x
f( f⁻¹(x) ) = x.
