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Let \( f: R \rightarrow[-1,1] \) and \( g: R \rightarrow B \), where \( R \) be the set of all real numbers and \( g(x)= \)
P \( \sin ^{-1}\left(\frac{f(x)}{2} \sqrt{4-f^{2}(x)}\right)+\frac{\pi}{3} \). If \( y=f(x) \) and \( y=g(x) \) are both surjective, then \( \operatorname{set} B \) is given by :
(a) \( \left[-\frac{\pi}{3}, \frac{\pi}{3}\right] \)
(b) \( \left[0, \frac{2 \pi}{3}\right] \)
(c) \( \left[0, \frac{\pi}{3}\right] \)
(d) \( [0, \pi] \)
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