The range of the real valued function $f(x)=\frac{1}{x-|x|}$ is

• A

  $(0, \infty)$
• Correct answer
  B

  $(-\infty, 0)$
• C

  $(-\infty, 0) \cup(0, \infty)$
• D

  $(-\infty, \infty)$

Solution

$f(x)=\frac{1}{x-|x|}$ For $x \geq 0, x-|x|=0 \Rightarrow \mathrm{f}(\mathrm{x}) \rightarrow \infty$
$\begin{array}{ll}\therefore & x < 0,|x|=-x \\ \Rightarrow & f(x)=\frac{1}{2 x} \\ \therefore & \text { Range } \in(-\infty, 0)\end{array}$

Hence, the correct answer is option: 'B'.