How can I disprove that if the composition of two functions is an injection then the two original functions...?

Let f,g be injective; to show: that f(g) is injective. If a,b are in the domain of g, and a is not equal to b, then g(a) is not equal to g(b), since g is injective. But now g(a) and g(b) are in the domain of f, and they are not equal to each other, and f is injective, so..... (you should be able to finish I hope)