If ##f## is a one-to-one function such that ##f(2)=9##, what is ##f^-1(9)##?

##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##.