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Question
The domain of the function defined by f(x) = `sin^-1 sqrt(x- 1)` is ______.
Options
[1, 2]
[–1, 1]
[0, 1]
None of these
Solution
The domain of the function defined by f(x) = `sin^-1 sqrt(x- 1)` is [1, 2].
Explanation:
Let f(x) = `sin^-1 sqrt(x - 1)`
∵ `sqrt(x - 1) ≥ 0` and `-1 ≤ sqrt(x - 1) ≤ 1`
⇒ 0 ≤ x – 1 ≤ 1
⇒ 1 ≤ x ≤ 2
⇒ `x ∈ [1, 2]`
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