Q221 / 270 · NDA 2016 (Phase 2) · Mathematics

What is the domain of the function $f(x)=\frac{1}{\sqrt{|x|-x}}$ ?

  • Correct answer
    A
    $(-\infty, 0)$
  • B
    $(0, \infty)$
  • C
    $0 \lt x \lt 1$
  • D
    $x \gt 1$

Solution

We know that $|x|=\left\{\begin{array}{cc} x, & x \geq 0 \\ -x, & x \lt 0 \end{array}\right.$ For domain, $|x|-x \gt 0$ Case 2: $x \lt 0$ Case 1: $x \gt 0 \Rightarrow x-x=0$ (not possible) $\begin{aligned} & -x-x \gt 0 \\ & \Rightarrow-2 x \gt 0 \\ & \Rightarrow x \lt 0 \end{aligned}$ So, $x \in(-\infty, 0)$

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

Relevant Questions