If 𝑓 is a one-to-one function such that 𝑓(2)=11, what is 𝑓−1(11)?

Question

If 𝑓 is a one-to-one function such that 𝑓(2)=11,(2)=11, what is 𝑓−1(11)?

Answer 1

If f is one-to-one and if f(a) = b, then f^-1(b) = a. In other words, if (a,b) is in the graph of y = f(x), then (b,a) is in the graph of y = f^-1(x).

So, since f(2) = 11, f^-1(11) = 2.

Answer 2

If 𝑓(2) = 11, this means 𝑓−1(𝑓(2)) = 𝑓−1(11)

But 𝑓−1(𝑓(2)) = 2

So 𝑓−1(11) = 2