If \( f(x)=2 x+|x|, g(x)=\frac{1}{3}(2 x-|x|) \) and \( h(x)=f(g(x)) \) then domain of \( \sin ^...
If \( f(x)=2 x+|x|, g(x)=\frac{1}{3}(2 x-|x|) \) and \( h(x)=f(g(x)) \) then domain of \( \sin ^{-1} \underbrace{(h(h(h(h \ldots h(x) \ldots))))}_{n \text { times }} \) is
(A) \( [-1,1] \)
(B) \( \left[-1,-\frac{1}{2}\right] \cup\left[\frac{1}{2}, 1\right] \)
(C) \( \left[-1,-\frac{1}{2}\right] \)
(D) \( \left[\frac{1}{2}, 1\right] \)
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