Question

If f(7)=22, then f^-1(f(7))=?

Answer 1

Rule: If f has an inverse, then

\[\Large f^{-1}(f(x)) = x\]

and

\[\Large f(f^{-1}(x)) = x\]

what does this mean in english? It means that the two functions (f and its own inverse) effectively cancel each other out. One takes a step forward, but the inverse takes a step back right to square one

Answer 2

Example:

f(3) = 5 is given

f^-1(5) = 3 takes us back to the initial input of 3

so

f(f^-1(3)) = 3
f^-1(f(3)) = 3