Q. If $f(x) = \left( \frac{x}{1 - |x|} \right)^{1/2002}$, then $D_{f}$ is
A) $R - \lbrack - 1,\ 1\rbrack$
B) $( - \infty,\ 1)$
C) $( - \infty,\ - 1) \cup (0,\ 1)$
D) None of these
Explanation
(c)
For $f(x)$ to be defined, $\frac{x}{1 - |x|} > 0$
$ie,\ \ \ \ \ x > 0,\ \ \ \ 1 - |x| > 0$ or $x < 0,\ \ \ 1 - |x| < 0$
$\Rightarrow \ \ \ \ x \in (0,\ 1)$ or $x \in ( - \infty,\ - 1)$
$\therefore\ \ \ x \in ( - \infty,\ - 1) \cup (0,\ 1)$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.