Question

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

(a) (– 1, 0) ∪ (1, 2) 

(b) (1, 2) ∪ (2, ∞) 

(c) (– 1, 0) ∪ (1, 2) ∪ (2, ∞) 

(d) (1, 2)

Answer 1

Correct option (c) (– 1, 0) ∪ (1, 2) ∪ (2, ∞)

Explanation:

The expression log₁₀(x³ – x) is defined for

(x³ – x) > 0 x (x² – 1) > 0 

x (x + 1)(x – 1) > 0 x ∈(–1, 0) ∪ (1, ∞)

Also, the function 3/(4 – x²)  is defined only when

x ≠ ±2

Thus, D_f = (– 1, 0) ∪ (1, ∞) – {2}

= (–1, 0) ∪ (1, 2) ∪ (2, ∞)