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If f(x)=2x+abs(x),g(x)=1/3(2x-abs(x)) an...

If `f(x)=2x+abs(x),g(x)=1/3(2x-abs(x))` and h(x)=f(g(x)), domain of `underbrace(sin^(-1)(h(h(h(h...h(x)...)))))_("n times")` is

A

[-1,1]

B

`[-1,-1/2] cup [1/2,1]`

C

`[-1,-1/2]`

D

`[1/2,1]`

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A
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