Is $\sqrt{x^3}$ uniformly continuous?

Question

$f(x) = \sqrt{x^3}, x \in (2,3)$ and $ g(x) = x^3, x \in \Bbb R$.

I have showed that $g$ is not uniformly continuous, but unable to do the 1st one i.e. $f(x) = \sqrt{x^3}, x \in (2,3)$.

Need some help for that part!

Answer 1

$f$ (same formula) is continuous on $[2,3]$ hence uniformly continuous on it (by compactness of $[2,3]$) and its subspaces (by definition uniform continuity inherits to subspaces).

Answer 2

Hint. Any function which is continuous in a compact set is also uniformly continuous there and in any of its subsets.