Math Help - Proof regarding 1-1 functions

1. Proof regarding 1-1 functions

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

Take $g(x)=x^2$ and $f(x)=e^x$. The key is considering $f$ such that $g$ is injective restricted to the range of $f$, but not in all the domain of $g$. You can easily construct a los of these examples if you understand properly why this one works.