# Quick Continuity question

1. Apr 9, 2010

### kevinlightman

1. The problem statement, all variables and given/known data

Prove that if g:R->R is continuous at a then f(x,y)=g(x) is continuous at (a,b) $$\forall$$ b $$\in$$ R

2. Relevant equations

3. The attempt at a solution

So we know
$$\forall$$e>0 $$\exists$$d>0 s.t. $$\forall$$x$$\in$$R where |x-a|<d we have |g(x) - g(a)|<e
So I've said as $$\forall$$b$$\in$$R g(x)=f(x,y) & g(a)=f(a,b), these can be substituted in giving the expression we need except for the condition that [(x-a)2 + (y-b)2]1/2<d.
This seems to be an incorrect cheat though, am I along the right lines or not?

2. Apr 9, 2010

### Office_Shredder

Staff Emeritus
You are looking at the right line of thought.

If |(x,y)-(a,b)|<d, what can you say about |x-a|?