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JEE Main
Exam
JEE Main
Subject
Mathematics
Chapter
Inverse Trigonometric Functions

JEE Main · Mathematics · Inverse Trigonometric Functions

The natural domain of the function& f(x) = ^ - 1 (2x) + (π)/(3) is

The natural domain of the function& f(x)=sin⁡−1(2x)+π3f\left(x\right) = \sqrt{\sin^{- 1} \left(2x\right) + \dfrac{\pi}{3}} is

Options

  1. A[−12,12]\left[- \dfrac{1}{2}, \dfrac{1}{2}\right]
  2. B[−34,12]\left[- \dfrac{\sqrt{3}}{4}, \dfrac{1}{2}\right]
  3. C[134,12]\left[\dfrac{13}{4}, \dfrac{1}{2}\right]
  4. D[−32,1]\left[- \dfrac{\sqrt{3}}{2}, 1\right]

Correct answer

B. [−34,12]\left[- \dfrac{\sqrt{3}}{4}, \dfrac{1}{2}\right]

Step-by-step solution

Here,& 2x∈2x \in\left[-1,1\right]andand\sin^{- 1} \left(2x\right) +\dfrac{π}{3} \ge00
Hence,~x∈[−12,12]andx \in \left[- \dfrac{1}{2}, \dfrac{1}{2}\right]andx \ge - \dfrac{\sqrt{3}}{4}<br />So the domain is \left[-\dfrac{\sqrt{3}}{4}, \dfrac{1}{2}\right]
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