The domain of the function f(x)=(1/√[x]2-[x]-2) is Here [x] denotes the greatest integer not exceeding the value of [x]

Question

The domain of the function f(x)=(1/√[x]2-[x]-2) is Here [x] denotes the greatest integer not exceeding the value of [x] (A) (-∞,-2) ∪(1, ∞) (B) (-∞,-2) ∪(0, ∞) (C) (-∞,-2) ∪(2, ∞) (D) (-∞,-1) ∪(3, ∞)

Tardigrade Admin · Accepted Answer

We have, f(x)=(1/√[x]2-[x]-2) f(x) is defined when [x]2-[x]-2 > 0 ([x]-2)([x]+1) > 0 [x]>2 and [x]<-1 x ≥ 3 and x < -1 ∴ Domain of f(x) is x ∈(-∞,-1) ∪(3, ∞)

Q. The domain of the function $f (x) = \frac{1}{[ x ] ^{2} - [ x ] - 2}$ is
Here $[x]$ denotes the greatest integer not exceeding the value of $[x]$

$(- \infty, - 2) \cup (1, \infty)$

$(- \infty, - 2) \cup (0, \infty)$

$(- \infty, - 2) \cup (2, \infty)$

$(- \infty, - 1) \cup (3, \infty)$

We have,
$f (x) = \frac{1}{[ x ] ^{2} - [ x ] - 2}$
$f (x)$ is defined when
$[x]^{2} - [x] - 2 > 0$
$([x] - 2) ([x] + 1) > 0$
$[x] > 2$ and $[x] < - 1$
$x \geq 3$ and $x < - 1$
$∴$ Domain of $f (x)$ is $x \in (- \infty, - 1) \cup (3, \infty)$

Q. The domain of the function f(x)=[x]2−[x]−2​1​ is Here [x] denotes the greatest integer not exceeding the value of [x]

(−∞,−2)∪(1,∞)

(−∞,−2)∪(0,∞)

(−∞,−2)∪(2,∞)

(−∞,−1)∪(3,∞)