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The domain set of the function f ( x ) = tan − 1 x − cot − 1 x + cos − 1 ( 2 − x ) is

Options

  1. A0 , 1
  2. B[ - 1, 1 ]
  3. C1 , 3
  4. DNone of these

Correct answer

C. 1 , 3

Step-by-step solution

Since, tan - 1 ⁡ x and cot - 1 ⁡ x exists for all x ∈ R and cos - 1 ⁡ 2 - x exist if - 1 ≤ 2 - x ≤ 1 ⇒ 1 ≤ x ≤ 3 Thus, the domain of the given function is [ 1 , 3 ] .

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