Domain of the function f(x)=(1/√[x]2-[x]-6) where [x] is greatest integer ≤ x is

Question

Domain of the function f(x)=(1/√[x]2-[x]-6) where [x] is greatest integer ≤ x is (A) (-∞,-2) ∪[4, ∞] (B) (-∞,-2) ∪[3, ∞] (C) [-∞,-2] ∪[4, ∞] (D) [-∞,-2] ∪(3, ∞)

Tardigrade Admin · Accepted Answer

[x2]-[x]-6>0 ([x]-3)([x]+2)>0 [x]<-2,[x]>3 ⇒ x ∈(-∞,-2) ∪[4, ∞)

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

$(- \infty, - 2) \cup [4, \infty]$

$(- \infty, - 2) \cup [3, \infty]$

$[- \infty, - 2] \cup [4, \infty]$

$[- \infty, - 2] \cup (3, \infty)$

$[x^{2}] - [x] - 6 > 0 ([x] - 3) ([x] + 2) > 0$
$[x] < - 2, [x] > 3$
$\Rightarrow x \in (- \infty, - 2) \cup [4, \infty)$

Q. Domain of the function f(x)=[x]2−[x]−6​1​ where [x] is greatest integer ≤x is

(−∞,−2)∪[4,∞]

(−∞,−2)∪[3,∞]

[−∞,−2]∪[4,∞]

[−∞,−2]∪(3,∞)