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NDA 2019 Maths · Mathematics · Inverse Trigonometric Functions · easy

The domain of the function f(x)=sin ^-1(2x-1) is

Single correct option

The domain of the function f(x)=sin⁡−1(2x−1)f(x)=\sin^{-1}(2x-1) is
  1. A. [−1,1][-1,1]
  2. B. [−12,12]\left[-\dfrac12,\dfrac12\right]
  3. C. [0,1][0,1]
  4. D. [0,2][0,2]
Show answer and solution

Answer: (C) [0,1][0,1]

The inverse sine is defined only when its argument lies in [−1,1][-1,1]. So −1≤2x−1≤1-1\le2x-1\le1, which gives 0≤2x≤20\le2x\le2 and 0≤x≤10\le x\le1. The domain is [0,1][0,1]. The option [−1,1][-1,1] is the domain of sin⁡−1x\sin^{-1}x itself, not of the composite.
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Original question written in the NDA 2019 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake