Hint:

Maybe it is better to start with a contradiction.

Let . Then there exists a x1 such that f(x1) = x2 and x1<>x2

fof(x1) = f(x1) ---- by your definition of f

also fof(x1) = f(f(x1)) = f(x2)

thus f(x1) = f(x2) => f is not one-to-one

Can you try to complete?