# Math Help - f/g if both are uniformly continuous

1. ## f/g if both are uniformly continuous

Is it true or false that for any two uniformly continuous functions f and g on a set D such that g(x)=/=0 on all of D the function f/g is uniformly continuous on D? If yes, prove, if not show a counterexample. What if D is compact?

Thanks!

2. How about $f(x)=1$ and $g(x)=x$, defined on $(0,\infty)$? Those two functions are uniformly continuous, but the function $f(x)/g(x)=1/x$ is not.

For the second question, you should ask yourself if there are any properties for continuous functions on compact sets.