Question

Domain of definition of the function f(x) = 3/(4 - x²) + log₁₀(x³ - x) is

(a) (-1, 0) ∪ (1, 2) ∪ (2, ∞) 

(b) (-1, 0) ∪ (1, 0) 

(c) (-2, 2) 

(d) (1, 2) ∪ (2, ∞)

Answer 1

The correct option (a) (-1, 0) ∪ (1, 2) ∪ (2, ∞) 

Explanation:

 is define when(x ≠ 2) and x³ – x > 0 

i.e. x(x² – 1) > 0 ⇒ x > 0 and x² > 1 or x < 0 and x² – 1 < 0 

⇒ x > 0 and x > 1 or x < 0 and x > – 1 

∴ Domain of f = (–1, 0) ∪ (1, 2) ∪ (2, ∞)