Q225 / 270 · NDA 2015 (Phase 2) · Mathematics
The domain of the function $f(x)=\frac{1}{\sqrt{|x|-x}}$ is
- A$[0, \infty)$
- Correct answerB$(-\infty, 0)$
- C$[1, \infty)$
- D$(-\infty, 0]$
Solution
$\begin{aligned}
& f(x)=\frac{1}{\sqrt{|x|-x}} \\
& |x|-x \neq 0
\end{aligned}$
So $\mathrm{x} \lt 0$....(1)
$\mathrm{x}=(-\infty, 0)$
again $|x|-x \gt 0$
$|\mathrm{x}| \gt \mathrm{x}$
it is possible only when $x$ is negative.
$x=(-\infty, 0)$....(2)
So from eq. (1) \& eq. (2)
$\text { domain } \mathrm{x}=(-\infty, 0)$
Hence, the correct answer is option: 'B'.