Question

The domain of function is f(x) = `sqrt(-log_0.3(x - 1))/sqrt(x^2 + 2x + 8)` is ______.

Options

• (1, 4)

• (–2, 4)

• (2, 4)

• [2, ∞)

Answer 1

The domain of function is f(x) = `sqrt(-log_0.3(x - 1))/sqrt(x^2 + 2x + 8)` is [2, ∞).

Explanation:

For x² + 2x + 8 > 0  ...(here D = 4 – 8(4) < 0)

∴ x² + 2x + 8 > 0   ....(∀ x ∈ R)

– log_0.3(x – 1) ≥ 0

⇒ log_0.3(x – 1) ≤ 0

⇒ (x – 1) ≥ 1

⇒ x ≥ 2

∴ R ∩ [2, ∞) = [2, ∞)