g of f injective, but g not injective

gotmilk04

1. The problem statement, all variables and given/known data
Give an example of a map f:A[tex]\rightarrow[/tex]B and a map g:B[tex]\rightarrow[/tex]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

Mark44

In a nutshell, find two functions, f and g, so that g [itex]\circ [/itex] f is one-to-one, but f [itex]\circ [/itex] 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.