Let \( f(x)=\tan ^{-1}(g(x)) \), where \( g(x) \) is monotonically increasing for \( 0x\frac{\pi...

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Let \( f(x)=\tan ^{-1}(g(x)) \), where \( g(x) \) is monotonically increasing for \( 0x\frac{\pi}{2} \). Then, \( f(x) \) is
(a) increasing on \( (0, \pi / 2) \)
(b) decreasing on \( (0, \pi / 2) \)
(c) increasing on \( (0, \pi / 4) \) and decreasing on \( (\pi / 4, \pi / 2) \)
(d) none of these
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