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NTA Abhyas JEE Main2020MathematicsInverse Trigonometric FunctionsPractice

If f x = t a n - 1 ln e 2 / x 3 ln e 2 x 3 + t a n - 1 ln e 2 x 3 ln e / x 6   ∀ x ≥ e , then the incorrect statement is

Options

  1. Af x is a constant function
  2. Bf x ≥ 0
  3. Cf x is an even function
  4. Df x ≥ π

Correct answer

C. f x is an even function

Step-by-step solution

We have, f x = t a n - 1 2 - 3 ln ⁡ x 2 + 3 ln ⁡ x + t a n - 1 2 + 3 ln ⁡ x 1 - 6 ln ⁡ x = t a n - 1 2 - t a n - 1 3 ln ⁡ x + t a n - 1 2 + t a n - 1 3 ln ⁡ x + π Using, tan - 1 A - tan - 1 B = tan - 1 A - B 1 + A B and tan - 1 A + tan - 1 B = tan - 1 A + B 1 - A B + π   ∵ A B > 1 , we get, f x = t a n - 1 2 + t a n - 1 2 + π = constant

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