Let $$f(x) = \sin \left(\frac{\pi}{6}\sin\left(\frac{\pi}{2}\sin x\right)\right)$$ for all $$x \in R$$ and $$g(x) = \frac{\pi}{2} \sin x$$ for all $$x \in R$$. Let (f o g)(x) denote f(g(x)) and (g o f)(x) denote g(f(x)). Then which of the following is (are) true?

A

Range of f is $$\left[-\frac{1}{2}, \frac{1}{2}\right]$$

B

Range of f o g is $$\left[-\frac{1}{2}, \frac{1}{2}\right]$$

C

$$\lim_{x \rightarrow 0}\frac{f(x)}{g(x)} = \frac{\pi}{6}$$

D

There is an $$x \in R$$ such that (g o f)(x) = 1