$\displaystyle g$ is an element of group $\displaystyle G$. $\displaystyle f(g)$ is a homomorphism from $\displaystyle G$ to $\displaystyle H$. Prove that $\displaystyle f(g^{-1})=f(g)^{-1}$.

I'm told the proof is by multiplying the two terms, like this (I guess)

$\displaystyle f(g^{-1}) f(g)^{-1} = ??$

but still cannot see what to do.

I also have that $\displaystyle e_G, e_H$, are the identities in $\displaystyle G$ and $\displaystyle H$, respectively.