Firstly, i'm sorry if this is the wrong forum. It seems to be analysis, but it is in a calculus book so wasn't sure.

I'm stuck on this question:

Prove that if $\displaystyle g:\mathbb{R} \rightarrow \mathbb{R}$ is continuous at $\displaystyle a$ then $\displaystyle f(x,y)=g(x)$ is continuous at (a,b) for all $\displaystyle b \in \mathbb{R}$

If someone could just give me an idea of how to start the proof. I understand the definition for continuity.