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Question
Find the domain of sin–1 (x2 – 4).
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Solution
–1 ≤ (x2 – 4) ≤ 1
`\implies` 3 ≤ x2 ≤ 5
`\implies sqrt(3) ≤ |x| ≤ sqrt(5)`
`\implies x ∈ [-sqrt(5), -sqrt(3)] ∪ [sqrt(3), sqrt(5)]`.
So required domain is `[-sqrt(5), -sqrt(3)] ∪ [sqrt(3), sqrt(5)]`.
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