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 (fog) \( (x) \) dentoe \( f(g(x)) \)
\( \mathrm{P} \) and (gof) \( (x) \) 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 fog is \( \left[-\frac{1}{2}, \frac{1}{2}\right] \)
(C) \( \quad \lim _{x \rightarrow 0} \frac{f(x)}{g(x)}=\frac{\pi}{6} \)
(D) There is an \( x \in R \) such that (gof) \( (x)=1 \)
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