I have to prove the following:

Suppose that functionsfandgare continuous at $\displaystyle x=c\in (a,b)$ and f(c) > g(c). Prove there exists $\displaystyle \delta$ > 0 such that for all $\displaystyle x\in (a,b)$ with $\displaystyle |x-c|<\delta$, we have f(x) > g(x).

I really have no idea. any help on this would be great thanks!