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NTA Abhyas JEE Main2020MathematicsInverse Trigonometric FunctionsPractice

The domain of the function f x = 4 cos - 1 ⁡ 1 - x 2 is

Options

  1. A- ∞ , - 3 ∪ 3 , ∞
  2. B- 3,3
  3. C- ∞ , - 3 ∪ 3 , ∞
  4. Dϕ

Correct answer

B. - 3,3

Step-by-step solution

cos - 1 ⁡ 1 - x 2 is defined if - 1 ≤ 1 - x 2 ≤ 1 ⇒ - 2 ≤ 1 - x ≤ 2 ⇒ - 3 ≤ - x ≤ 1 ⇒ - 1 ≤ x ≤ 3 x ≥ - 1 is true for all real values of x . x ≤ 3 ⇒ - 3 ≤ x ≤ 3 Also, 4 cos - 1 ⁡ 1 - x 2 is defined if cos - 1 ⁡ 1 - x 2 ≥ 0 ⇒ 1 - x 2 ≥ cos ⁡ 0 = 1 ⇒ 1 - x ≥ 2 ⇒ x ≤ - 1 (not possible) ∴ Domain of f x = - 3,3

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