Q. If $f(x) = \frac{1}{\sqrt{|x| - x}}$ then, domain of $f(x)$ is
A) $( - \infty,\ 0)$
B) $( - \infty,\ 2)$
C) $( - \infty,\ \infty)$
D) None of the above
Explanation
(a)
$f(x)$ is defined
When $|x| > x$
$\Rightarrow \ \ \ \ \ \ \ x < - x,\ x > x$
$\Rightarrow \ \ 2x < 0,\ (x > x\$is not possible$)$
$\Rightarrow \ \ \ \ x < 0$
Hence domain of $f(x)$ is $( - \infty,\ 0)$.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.