CUET · MATHS · PYQ PAPER 2025
The domain of \(y=\cos ^{-1}\left(x^2-4\right)\) is
- A \([0, \pi]\)
- B \([-\sqrt{5},-\sqrt{3}] \cup[\sqrt{3}, \sqrt{5}]\)
- C \([-\sqrt{5},-\sqrt{3}] \cap[-\sqrt{5}, \sqrt{3}]\)
- D \([-1,1]\)
Answer & Solution
Correct Answer
(B) \([-\sqrt{5},-\sqrt{3}] \cup[\sqrt{3}, \sqrt{5}]\)
Step-by-step Solution
Detailed explanation
\(-1 \le x^2-4 \le 1\) \(-1+4 \le x^2 \le 1+4\) \(3 \le x^2 \le 5\) \(x^2 \ge 3 \implies x \le -\sqrt{3} \text{ or } x \ge \sqrt{3}\) \(x^2 \le 5 \implies -\sqrt{5} \le x \le \sqrt{5}\) \(x \in ([-\sqrt{5}, \sqrt{5}]) \cap ((-\infty, -\sqrt{3}] \cup [\sqrt{3}, \infty))\)…
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