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

1 Answer
Mar 31, 2016

Answer:

#f^(-1)(9) = f^(-1)(f(2)) = 2#

Explanation:

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#.