Question

Domain of the function f(x) = `sqrt(1 + 4x - x^2)` is ______

Options

• `-sqrt5 ≤ x ≤ sqrt5`

• 2 - `sqrt5 ≤ x ≤ 2 + sqrt5`

• -2 ≤ x ≤ 2

• -2 `+ sqrt5 ≤ x ≤ -2 - sqrt5`

Answer 1

Domain of the function f(x) = `sqrt(1 + 4x - x^2)` is `underline(2 - sqrt5 ≤ x ≤ 2 + sqrt5)`.

Explanation:

The quantity under root is positive when 1 + 4x - x² ≥ 0

i.e. 5 - (x - 2)² ≥ 0

2 - `sqrt5 ≤ x ≤ 2 + sqrt5`