Question 3
FunctionsThe function f: x → √(x2 + 5x − 6) is defined on the set of real numbers R. Find the domain of f.
- A.{x : x ∈ R, x ≤ −6, x ≥ −1}
- B.{x : x ∈ R, x ≤ −6, x ≥ 1}
- C.{x : x ∈ R, x ≤ ⅙, x ≥ 1}
- D.{x : x ∈ R, x ≤ −6, x ≥ ⅙}
Show the answer and explanation
Answer: B ({x : x ∈ R, x ≤ −6, x ≥ 1})
Explanation
The square root needs x² + 5x − 6 ≥ 0, i.e. (x + 6)(x − 1) ≥ 0. This holds when x ≤ −6 or x ≥ 1.