The natural domain of the function f x = sin - 1 ⁡ 2 x + π 3 is

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Question: Answered & Verified by Expert

The natural domain of the function

f (x) = \sqrt{\sin^{- 1} (2 x) + \frac{π}{3}}

is

MathematicsInverse Trigonometric FunctionsJEE Main

Options:

A $[- \frac{1}{2}, \frac{1}{2}]$
B $[- \frac{\sqrt{3}}{4}, \frac{1}{2}]$
C $[\frac{13}{4}, \frac{1}{2}]$
D $[- \frac{\sqrt{3}}{2}, 1]$

Solution:

2884 Upvotes Verified Answer

The correct answer is:

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

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}]

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