Hey all, can't figure out how to lay out the proof for the following problem:

If f: A -> B is surjective and g: B -> C is surjective then g o f : A -> C is surjective.

well by definition, for all b ∈ B there exists a ∈ A such that f(a) = b

and, for all c ∈ C there exists b ∈ B such that g(b) = c

Any help would be appreciated!