Question

Find the domain of the function f given by f(x) = `1/sqrt([x]^2 - [x] - 6)`

Answer 1

Given that f(x) = `1/sqrt([x]^2 - [x] - 6)`

f is defined if [x]² – [x] – 6 > 0

or ([x]–3) ([x] + 2) > 0

⇒ [x] < – 2 or [x] > 3

⇒ x < – 2 or x ≥ 4

Hence Domain = `(-oo, -2) ∪ [4, oo)`.