Question

The domain of the function f(x) = log_3+x (x² - 1) is ______.

Options

• (- 3, - 1) ∪ (1, ∞)

• [- 3, - 1) ∪ [1, ∞)

• (- 3, - 2) ∪ (- 2, - 1) ∪ (1, ∞)

• [- 3, - 2) ∪ (- 2, - 1) ∪ [1, ∞)

Answer 1

The domain of the function f(x) = log_3+x (x² - 1) is (- 3, - 2) ∪ (- 2, - 1) ∪ (1, ∞).

Explanation:

f(x) is to be defined when x² - 1 > 0

⇒ x² > 1, ⇒ x < - 1 or x > 1 and 3 + x > 0

∴ x > - 3 and x ≠ - 2

∴ D_f = (- 3, - 2) ∪ (- 2, - 1) ∪ (1, ∞)