Disprove that the composition of a surjection(onto), then the original two functions must be be onto.?

Proof by counter example: let g = |x| be a function from the reals to the reals; it is not surjective. Let f = x^2 be a function from the reals to the non-negative reals; it is surjective. Now consider f(g) , a function from the reals to the non-negative reals; is it surjective?