Question

Find the domain of following functions :

f(x) = 3/√4 - x² log(x³ - x)

Answer 1

Domain of √4 − x²  is [−2, 2] but √4 − x² = 0 for x = ± 2 ⇒ x ∈ (–2, 2) log(x³ − x) is defined for x³ − x > 0 i.e. x(x − 1)(x + 1) > 0. 

∴ domain of log(x³ − x) is (−1, 0 ) ∪ (1, ∞). 

Hence the domain of the given function is {(−1, 0 ) ∪ (1, ∞)}∩ (−2, 2) = (−1, 0 ) ∪ (1, 2).