Proving Continuity for Composition of Functions: f(x,y)=g(x)

[kevinlightman]

Homework Statement

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

Homework Equations

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?

 

[Office_Shredder]

You are looking at the right line of thought.If |(x,y)-(a,b)|<d, what can you say about |x-a|?