Consider \( f, g \) and \( h \) be three real valued functions defined on \( R \). Let \( f(x)=\...

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Consider \( f, g \) and \( h \) be three real valued functions defined on \( R \).
Let \( f(x)=\left\{\begin{aligned}-1, & x0 \\ 0, & x=0, g(x)=x\left(1-x^{2}\right) \text { and } h(x) \text { be such that } \\ 1, & x0 \end{aligned}\right. \) \( h^{\prime \prime}(x)=6 x-4 \).
Also, \( h(x) \) has local minimum value 5 at \( x=1 \).
Range of function \( \sin ^{-1} \sqrt{(f o g(x))} \) is
(a) \( (0, \pi / 2) \)
(b) \( \{0, \pi / 2\} \)
(c) \( \{-\pi / 2,0, \pi / 2\} \)
(d) \( \{\pi / 2\} \)
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