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] − [1/ 2 ] ∪ [ 1/ 2 , 1 ](c) [ − 1 , − 1/ 2 ](d) [ 1/ 2 , 1 ]

A

[-1,1]

B

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

C

`[-1,-1/2]`

D

`[1/2,1]`

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The correct Answer is:

A

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