Proving the Identity Function: Composed Functions

[andmcg]

Suppose that f composed with g equals g composed with f for all functions g. Show that f is the identity function.

I really just don't know where to start.

 

[Fredrik]

*Deleted*

That was probably a bad tip. I'll try to think of something better.

OK, here we go...

If f isn't the identity, there's an x such that f(x)≠x. Now choose a g that contradicts that.