G of f injective, but g not injective

[gotmilk04]

Homework Statement

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.

Homework Equations

The Attempt at a Solution

I'm not really sure what they are asking for.

 

[Mark44]

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

 

[gotmilk04]

So it's basically just guess and check?

 

[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.