Thread: Proof regarding 1-1 functions

I want to disprove:
If g of f is one-to-one, then g is one-to-one.

Thanks for your help

Originally Posted by CoraGB

I have a similar problem, but in this case I want to disprove:
If g of f is one-to-one, then g is one-to-one.

Thanks for your help

Take and . The key is considering such that is injective restricted to the range of , but not in all the domain of . You can easily construct a los of these examples if you understand properly why this one works.