Two functions f/g Uniform Continuity

[Design]

I was wondering if f and g are two uniformly continuous functions on a set such that g(x) is not zero is f/g uniformly continuous?


I have a feeling it is not but I can't seem to find a counter example.

 

[micromass]

The function 1/x on ]0,1] should probably be a good counterexample...

 

[Design]

But 1 is not considering a function f is it?

 

[micromass]

Take f(x)=1, the constant function, and g(x)=x...

 

[Design]

If D is compact then f/g will be uniformly continuous on D right?

 

[micromass]

Yes. That's why I took the interval ]0,1].