# G of f injective, but g not injective

## 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.

## The Attempt at a Solution

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

## The Attempt at a Solution

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Mark44
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.

So it's basically just guess and check?

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.