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CUET · MATHS · PYQ PAPER 2023

The domain of \(y = \cos^{-1}(x^2 - 4)\) is:

  1. A [3, 5]
  2. B \([0, \pi]\)
  3. C \([-\sqrt{5},-\sqrt{3}] \cap[-\sqrt{5}, \sqrt{3}]\)
  4. D \([-\sqrt{5},-\sqrt{3}] \cup[\sqrt{3}, \sqrt{5}]\)
Verified Solution

Answer & Solution

Correct Answer

(D) \([-\sqrt{5},-\sqrt{3}] \cup[\sqrt{3}, \sqrt{5}]\)

Step-by-step Solution

Detailed explanation

Domain of \( \cos^{-1}(u) \) is \( -1 \le u \le 1 \). \( -1 \le x^2 - 4 \le 1 \) \( 3 \le x^2 \le 5 \) \( x^2 \ge 3 \implies x \le -\sqrt{3} \text{ or } x \ge \sqrt{3} \) \( x^2 \le 5 \implies -\sqrt{5} \le x \le \sqrt{5} \) Intersection:…