# Homework Help: G of f injective, but g not injective

1. Sep 29, 2009

### gotmilk04

1. The problem statement, all variables and given/known data
Give an example of a map f:A$$\rightarrow$$B and a map g:B$$\rightarrow$$C where g of f is injective but g is not injective.

2. Relevant equations

3. The attempt at a solution
I'm not really sure what they are asking for.
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Sep 29, 2009

### Staff: Mentor

In a nutshell, find two functions, f and g, so that g $\circ$ f is one-to-one, but f $\circ$ g is not.

3. Sep 29, 2009

### gotmilk04

So it's basically just guess and check?

4. Sep 29, 2009

### aPhilosopher

It doesn't have to be. Think about arranging it so that g is injective on the image of f but not on the entire domain of g.