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NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Mathematics
Chapter
Inverse Trigonometric Functions

NTA Abhyas 2020 · Mathematics · Inverse Trigonometric Functions

The domain set of the function f( x ) = ^ -1 x - ^ -1 x + ^ -1 ( 2...

The domain set of the function f(x)=tan⁡−1x−cot⁡−1x+cos⁡−1(2−x)f( x ) = \tan^{-1} x - \cot^{-1} x + \cos^{-1} ( 2 - x ) is

Options

  1. A[0,1]\left[0, 1\right]
  2. B[−1,1][ - 1, 1 ]
  3. C[1,3]\left[1, 3\right]
  4. DNone of these

Correct answer

C. [1,3]\left[1, 3\right]

Step-by-step solution

Since, tan⁡−1x\tan^{-1} x and cot⁡−1x\cot^{-1} x exists for all x∈x \inR and cos⁡−1\cos^{-1}\left(2 - x\right)existifexist if- 1 ≤ 2 - x ≤ 1<br/><br/><br /><br />⇒ 1 ≤ x ≤ 3<br/><br/>Thus,thedomainofthegivenfunctionis<br /><br />Thus, the domain of the given function is[1,3].
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