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QUESTION

# 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.