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The domain of $\sin^{- 1} [\log_{2} (x^{2} / 2)]$ is

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[−2,−1]

[1,2]

[−2,−1]∪[1,2]

[−2,0]

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detailed solution

Correct option is C

We know that domain of sin-1x is -1,1. ∴sin-1log2(x22)is defined if−1≤log2(x22)≤1 ⇒2−1≤x22≤2 ⇒1≤x2≤4 ⇒x∈-2,-1∪1,2

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The domain of sin−1[log2(x2/2)] is

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The domain of $\sin^{- 1} [\log_{2} (x^{2} / 2)]$ is