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Inverse Trigonometric Functions — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsInverse Trigonometric Functions1 Mark
MCQ
The domain of the function $\cos ^{-1}(2 x-1)$ is
  • ✓
    $[0,1]$
  • B
    $[-1,1]$
  • C
    $(-1,1)$
  • D
    $[0, \pi]$
✓

Answer

Correct option: A.
$[0,1]$
(a) : We know, $0 \leq \cos ^{-1}(2 x-1) \leq \pi$
$\Rightarrow-1 \leq 2 x-1 \leq 1 \Rightarrow 0 \leq 2 x \leq 2 \Rightarrow 0 \leq x \leq 1$
$\therefore$ Domain of $\cos ^{-1}(2 x-1)=[0,1]$

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