COMEDK · Maths · 24. Functions
The domain of the function \(f(x) = \sin^{-1}(\sqrt{x - 1})\)
- A \([1, 2]\)
- B \([0, 1]\)
- C \((-\infty, 1] \cup [2, \infty)\)
- D \([-1, 1]\)
Answer & Solution
Correct Answer
(A) \([1, 2]\)
Step-by-step Solution
Detailed explanation
For the function \(f(x) = \sin^{-1}(\sqrt{x - 1})\) to be defined, the argument of the inverse sine function must lie in the interval \([-1, 1]\). \(-1 \le \sqrt{x - 1} \le 1\) Since the principal square root is always non-negative, this inequality reduces to:…
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