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Question
The domain of y = cos–1(x2 – 4) is ______.
Options
[3, 5]
[0, π]
`[-sqrt(5), -sqrt(3)] ∩ [-sqrt(5), sqrt(3)]`
`[-sqrt(5), -sqrt(3)] ∪ [-sqrt(3), sqrt(5)]`
Solution
The domain of y = cos–1(x2 – 4) is `[-sqrt(5), -sqrt(3)] ∪ [-sqrt(3), sqrt(5)]`.
Explanation:
y = cos–1(x2 – 4)
⇒ cosy = x2 – 4
i.e. – 1 ≤ x2 – 4 ≤ 1 ......(Since – 1 ≤ cos y ≤ 1)
⇒ 3 ≤ x2 ≤ 5
⇒ `sqrt(3) ≤ |x| ≤ sqrt(5)`
⇒ `x∈ [-sqrt(5), -sqrt(3)] ∪ [-sqrt(3), sqrt(5)]`
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