Let \( S \) denotes the set consisting of four functions and \( S=\left\{[x], \sin ^{-1} x,|x|,\{x\}\right\} \) where, \( \{x\} \) denotes fractional part
\( \mathrm{P} \) and \( [x] \) denotes greatest integer function. Let \( A, B, C \) are subsets of \( S \).
W
Suppose
A : consists of odd function(s)
B : consists of discontinuous function(s)
and \( \mathrm{C} \) : consists of non-decreasing function(s) or increasing function(s).
If \( f(x) \in A \cap C ; g(x) \in B \cap C ; h(x) \in B \) but not \( C \) and \( l(x) \in \) neither \( A \) nor \( B \) nor \( C \).
Then, answer the following.
The range of \( f(h(x)) \) is
(a) \( \left(0, \frac{\pi}{2}\right) \)
(b) \( \left[0, \frac{\pi}{2}\right) \)
(c) \( \left(0, \frac{\pi}{2}\right] \)
(d) \( \left[0, \frac{\pi}{2}\right] \)
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