First slide

Functions (XII)

Question

The domain of the function $f (x) = \frac{1}{\sqrt{[x]^{2} - [x] - 6}} is$

Moderate

A

(– ∞, – 2) ∪ [4, ∞)
B

(– ∞, – 2] ∪ [4, ∞)
C

(– ∞, – 2) ∪ (4, ∞)
D

None of these

Solution

f (x) is defined for
$\begin{array}{l} [x]^{2} - [x] - 6 > 0 \Rightarrow ([x] - 3) ([x] + 2) > 0 \\ \Rightarrow [x] < - 2 or [x] > 3 \\ But [x] < - 2 \Rightarrow [x] = - 3, - 4, - 5, \dots \\ ∴ x < - 2 \\ Also, [x] > 3 \Rightarrow [x] = 4, 5, 6, \dots \\ ∴ x \geq 4 \\ ∴ Domain of f = (- \infty, - 2) \cup [4, \infty) \end{array}$

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