Let $\displaystyle R$ be a ring and $\displaystyle M$ an $\displaystyle R$-module.

$\displaystyle Hom_R(R,M)$ is the set of $\displaystyle R$-homomorphisms from $\displaystyle R$ to $\displaystyle M$.

Define $\displaystyle \phi: Hom_R(R,M) \rightarrow M$ by $\displaystyle \phi(f)=f(1)$. Show $\displaystyle \phi$ is a ring isomorphism.

I know how to show it is a homomorphism and one-to-one, but having trouble with onto. Can I get some help?