Properties of Composite Functions

Let the functions $f$ and $g$ be defined by $f(x)=\sqrt{x}$ and $g(x)=x^2$. Which of the following statements is/are true?

I. The expression $f(g(x))$ is equivalent to $|x|$.

II. The expression $g(f(x))$ is equivalent to $x$ for all $x \ge 0$.

III. The equation $f(g(x)) = g(f(x))$ holds for all values of $x$ for which both compositions are defined.