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Question
The domain of the function f defined by f(x) = `sqrt(4 - x) + 1/sqrt(x^2 - 1)` is equal to ______.
Options
`(– oo, – 1) ∪ (1, 4]`
`(– oo, – 1] ∪ (1, 4]`
`(– oo, – 1) ∪ [1, 4]`
`(– oo, – 1) ∪ [1, 4)`
Solution
The domain of the function f defined by f(x) = `sqrt(4 - x) + 1/sqrt(x^2 - 1)` is equal to `(– oo, – 1) ∪ (1, 4]`.
Explanation:
Given that: f(x) = `sqrt(4 - x) + 1/sqrt(x^2 - 1)`
f(x) is defined if
4 – x ≥ 0 or x2 – 1 > 0
⇒ – x ≥ – 4 or (x – 1)(x + 1) > 0
⇒ x ≤ 4 or x < – 1 and x > 1
∴ Domain of f(x) is `(– oo, – 1) ∪ [1, 4]`
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