Hi! Help me please to solve this.

Prove or disprove that:

1. If $\displaystyle f,g$ are uniformly continuous functions in $\displaystyle [0,\infty )$ then also$\displaystyle fg $ (product) is unif.continuous in $\displaystyle [0,\infty )$.

2. Same question, but about the composition of $\displaystyle f$ and $\displaystyle g$.

Thanks beforehand.