Uniform Continuity: Example of f*g Not Being Uniformly Continuous

[CarmineCortez]

Homework Statement

If f and g are uniformly continuous on X, give an example showing f*g may not be uniformly continuous.

The Attempt at a Solution

i think if the functions are unbounded the product will not uniformly continuous. Is there a specific example of this function..?

 

[pizzasky]

Consider some simple examples first!
Choose X = \mathbb{R}, and maybe let f(x) = x, for any x \in \mathbb{R}.