# How to prove that the composition of injection is an injection?

1. Aug 5, 2010

### jy02354441

how to prove it please?

2. Aug 6, 2010

### HallsofIvy

F(x) is "injective" if and only if f(x)= f(y) implies x= y.

Suppose both f(x) and g(x) are injective and F= f(g(x))

If F(x)= F(y) then f(g(x))= f(g(y)) so, since f is injective, we have g(x)= g(y). Now, since g is injective, ...