Let $f:\mathbb{R}\rightarrow \left [0,\infty \right )$ be a continuous function such that $g\left ( x \right )=(f\left ( x \right ))^2$ is uniformly continuous. Which of the following statements is always true ?
- $f$ is bounded
- $f$ may not be uniformly continuous
- $f$ is uniformly continuous
- $f$ is unbounded