Question

The domain of the function cos^-1 (log₂(x² + 5x + 8)) is

Options

• [2, 3]

• [-2, 2]

• [3, 1]

• [-3, -2]

Answer 1

[-3, -2]

Explanation:

- 1 ≤ log₂(x² + 5x + 8) ≤ 1

`=> 1/2 ≤ (x^2 + 5x + 8) ≤ 2`

`=> x^2 + 5x + 15/2 >= 0`

`=> x^2 + 2(5/2)x + (5/2)^2 - (5/2)^2 + 15/2 >=0`

`=> (x + 5/2)^2 + 5/4 >= 0 and x^2 + 5x + 6 <= 0`

⇒ (x + 3)(x + 2) ≤ 0

⇒ x ∈ [-3, -2]