Question

The domain of $f\left(x\right)=\frac{1}{\sqrt{|[|x|-1]|-5}}$ (where [.] represents greatest integer less than or equal to $x$) is

• A. $[-7,7]$
• B. $(-\infty ,7]$
• C. $(-\infty ,-7]$
• D. $[7,\infty )$

Answer 1

Answer: (C), (D)

The correct options are
C $(-\infty ,-7]$
D $[7,\infty )$

$|[|x|-1]|-5>0$
Let $y=[|x|-1]$
$\Rightarrow |y|>5$
$\Rightarrow y>5$ or $y<-5$
$\Rightarrow [|x|-1]>5$ or $[|x|-1]<5$
$\Rightarrow |x|-1\ge 6$ (or) $|x|-1<-5$
$\Rightarrow |x|>7$ (or) $|x|<-4$
$\because |x|$ can't be negative.
$\therefore x\in (-\infty ,-7]\cup [7,\infty )$