##f^(-1)(9) = f^(-1)(f(2)) = 2##
If ##f## is a one-to-one function then its inverse function ##f^(-1)## is well-defined.
What does the inverse do ? Exactly what it is called.
Suppose for example :
##f : RR rightarrow RR##
##x mapsto f(x) = y##
Then ##f^(-1)## do the opposite/reverse :
##f^-1 : RR rightarrow RR##
##y mapsto f^(-1)(y) = x##
Thus if ##f(x) = y## then ##f^(-1)(f(x)) = f^(-1)(y) = x##.
Therefore if ##f(2) = 9## you apply ##f^(-1)## to both sides and you get :
##f^(-1)(f(2)) = f^(-1)(9) = 2##.