COMEDK · Maths · 24. Functions
The domain of the function \(\sin ^{-1}\left(x^2-4\right)\) is
- A \(\left[-\dfrac{\pi}{2}, \dfrac{\pi}{2}\right]\)
- B \([-\sqrt{5},-\sqrt{3}] \cup[\sqrt{3}, \sqrt{5}]\)
- C \([3,5]\)
- D \([-\sqrt{5},-\sqrt{3}] \cap[\sqrt{3}, \sqrt{5}]\)
Answer & Solution
Correct Answer
(B) \([-\sqrt{5},-\sqrt{3}] \cup[\sqrt{3}, \sqrt{5}]\)
Step-by-step Solution
Detailed explanation
The domain of the function \(f(x) = \sin^{-1}(u)\) is defined by the condition \(-1 \le u \le 1\). For the given function \(f(x) = \sin^{-1}(x^2 - 4)\), we must have \(-1 \le x^2 - 4 \le 1\). Adding 4 to all parts of the inequality: \(3 \le x^2 \le 5\). This inequality implies…
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