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NDA 2020 Maths · Mathematics · Inverse Trigonometric Functions · medium

The domain of the function f(x)=sin ^-1(3x-2) is

Single correct option

The domain of the function f(x)=sin⁡−1(3x−2)f(x)=\sin^{-1}(3x-2) is
  1. A. [−1,1][-1,1]
  2. B. [13,1]\left[\dfrac13,1\right]
  3. C. [0,43]\left[0,\dfrac43\right]
  4. D. [13,23]\left[\dfrac13,\dfrac23\right]
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Answer: (B) [13,1]\left[\dfrac13,1\right]

sin⁡−1\sin^{-1} is defined for arguments in [−1,1][-1,1], so −1≤3x−2≤1-1\le3x-2\le1. Adding 22 gives 1≤3x≤31\le3x\le3, hence 13≤x≤1\frac13\le x\le1. Writing [−1,1][-1,1] confuses the domain of xx with that of 3x−23x-2.
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