Let f, g be continuous from $\displaystyle \mathbb{R}$ to $\displaystyle \mathbb{R}$ and suppose that f(r)=g(r) for all rational numbers r. Is it true that f(x)=g(x) for all $\displaystyle x \in \mathbb{R}$.

I think yes, but am having trouble formulating a proof. Here is what I have so far.

Assume for contradiction that it is not true. Then $\displaystyle \exists m \in \mathbb{R}/ \mathbb{Q} s.t. f(m) \neq g(m)$, but from here I can't see where to get the contradiction. Any help?