The domain of the function f (x) = log3 + x (x2 – 1) is(a) (– 3, �

1.	The domain of the function f (x) = log3 + 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» 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, ∞).

The domain of the function f (x) = log3 + 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»

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, ∞).