The domain of definition of function fx=sin-12x+π6for real values of x, is

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-14,12

-12,12

-12,14

-14,14

answer is A.

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Detailed Solution

Given,fx=sin-12x+π6To find domain, we must havesin-12x+π6≥0 but -π2≤sin-1θ≤π2Now, -π6≤sin-12x≤π2⇒sin-π6≤2x≤sinπ2⇒-12≤2x≤1⇒-14≤x≤12x∈-14,12

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