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CUET · MATHS · PYQ PAPER 2025

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

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

Answer & Solution

Correct Answer

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

Step-by-step Solution

Detailed explanation

\(-1 \le x^2-4 \le 1\) \(-1+4 \le x^2 \le 1+4\) \(3 \le x^2 \le 5\) \(x^2 \ge 3 \implies x \le -\sqrt{3} \text{ or } x \ge \sqrt{3}\) \(x^2 \le 5 \implies -\sqrt{5} \le x \le \sqrt{5}\) \(x \in ([-\sqrt{5}, \sqrt{5}]) \cap ((-\infty, -\sqrt{3}] \cup [\sqrt{3}, \infty))\)…