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The domain of definition of the function $f (x) = \sqrt{\sin^{- 1} (2 x) + \frac{π}{6}}$ for real-valued x is

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−14,12

−12,12

−12,19

−14,14

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Correct option is A

f(x)=sin−1⁡(2x)+π6 sin−1(2x)+π6≥0⇒sin-1(2x)≥-π6 2x≥sin-π6⇒2x≥-12⇒x≥-14and 2x≤1 x∈-14,12

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The domain of definition of the function f(x)=sin−1⁡(2x)+π6for real-valued x is

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The domain of definition of the function $f (x) = \sqrt{\sin^{- 1} (2 x) + \frac{π}{6}}$ for real-valued x is