Find the domain of the real valued function f(x)=([x2]-[x]-2)-1 / 2, where [.] is the greatest integer function

Question

Find the domain of the real valued function f(x)=([x2]-[x]-2)-1 / 2, where [.] is the greatest integer function (A) R-(-1,3] (B) R-[-1,3) (C) R-(-1,3) (D) R-[-1,3]

Tardigrade Admin · Accepted Answer

Let y=f(x)=([x]2-[x]-2)-1 / 2 ⇒ y2=(1/√[x]2-[x]-2) For real valued [x]2-[x]-2>0 ⇒ [x]-2 [x]+1 >0 [x] ∈ R-(-1,2) So, x ∈ R-(-1,3]

Q. Find the domain of the real valued function $f (x) = ([x^{2}] - [x] - 2)^{- 1/2}$ , where $[.]$ is the greatest integer function

$R - (- 1, 3]$

$R - [- 1, 3)$

$R - (- 1, 3)$

$R - [- 1, 3]$

Let $y = f (x) = ([x]^{2} - [x] - 2)^{- 1/2}$
$\Rightarrow y^{2} = \frac{1}{[ x ] ^{2} - [ x ] - 2}$
For real valued
$[x]^{2} - [x] - 2 > 0$
$\Rightarrow {[x] - 2} {[x] + 1} > 0$
$[x] \in R - (- 1, 2)$
So, $x \in R - (- 1, 3]$

Q. Find the domain of the real valued function f(x)=([x2]−[x]−2)−1/2, where [.] is the greatest integer function

R−(−1,3]

R−[−1,3)

R−(−1,3)

R−[−1,3]