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)`

Answer 1

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]`