The natural domain of the function fx=√(sin^(-1)⁡2x+π3) is

Correct answer: (B) -(√3)/4,1/2. Here, 2x∈-1,1 and sin^(-1)⁡2x+(π)/3≥0 Hence, x∈-1/2,1/2 and x≥-(√3)/4 So the domain is -(√3)/4,1/2

Q20 / 71 · NTA Abhyas (JEE Main) 2020 · Mathematics · Inverse Trigonometric Functions

The natural domain of the function $f (x) = \sqrt{\sin^{- 1} (2 x) + \frac{π}{3}}$ is

Here,

2 x \in [- 1,1]

and

\sin^{- 1} (2 x) + \frac{π}{3} \geq 0

Hence,

x \in [- \frac{1}{2}, \frac{1}{2}]

and

x \geq - \frac{\sqrt{3}}{4}

So the domain is

[- \frac{\sqrt{3}}{4}, \frac{1}{2}]

Hence, the correct answer is option: 'B'.