Question

Domain of the function f(x) = \(\frac{1}{\sqrt{[x]^2-[x]-6}}\) where [x] is greatest integer ≤ x is

• A. (-∞, -2) ∪ [4, ∞]
• B. (-∞, -2) ∪ [3, ∞]
• C. [-∞, -2) ∪ [4, ∞]
• D. [-∞, -2] ∪ [3, ∞)

Answer 1

The Correct Option is A

The function involves a square root and for it to be defined, the expression under the square root must be non-negative. Hence, we need: \[ [x]^2 - [x] - 6 \geq 0 \] Solving the inequality, we find that \( [x] \) must satisfy the condition \( [x] \leq -2 \) or \( [x] \geq 4 \).

Therefore, the domain of \( f(x) \) is \( (-\infty, -2) \cup [4, \infty) \), which is option (A).