Suppose $\displaystyle f: G \rightarrow H$ is a group homomorphism, $\displaystyle N \triangleleft G$, and $\displaystyle \text{ker}(f) \leq N$.

Prove that

$\displaystyle G/N \cong f(G)/f(N)$.

I don't see how to do this. Any hints would be nice. Thank you.