APFIVE 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.
A
All three statements are true.
B
Only Statements I and II are true.
C
Only Statements I and III are true.
D
Only Statement II is true.
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