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  4. Domain of definition of the function f(x) = √sin-1 (2x) + (π/6) for real valued x, is

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Q. Domain of definition of the function $f\left(x\right) = \sqrt{sin^{-1} \left(2x\right) + \frac{\pi}{6}}$ for real valued x, is

Relations and Functions - Part 2

Solution:

$-\frac{\pi}{6} \le sin^{-1}\left(2x\right) \le \frac{\pi}{2} \Rightarrow -\frac{1}{2} \le 2x \le 1 \Rightarrow x \in \left[-\frac{1}{4}, \frac{1}{2}\right]$