Question

The domain of the function f (x) = log_{3 + x} (x² – 1) is

(a) (– 3, – 1) ∪ (1, ∞) 

(b) [– 3, – 1] ∪ [1, ∞) 

(c) (– 3, – 2) ∪ (– 2, – 1) ∪ (1, ∞) 

(d) [– 3, – 2) ∪ (– 2, – 1) ∪ (1, ∞)

Answer 1

Answer: (c) (– 3, – 2) ∪ (– 2, – 1) ∪ (1, ∞)

The function is defined, when x² – 1 > 0, 3 + x > 0 and 3 + x ≠ 1 

⇒ x < – 1 or x > 1 and x > – 3 and x ≠ – 2 

∴ Domain of the function = (– 3, – 2) ∪ (– 2, – 1) ∪ (1, ∞).