Q42 / 160 · AP EAMCET 2021 (24 Aug Shift 2) · Mathematics

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

  • A
    $(0, \infty)$
  • Correct answer
    B
    $(-\infty, 0)$
  • C
    $\frac{(-\infty, \infty)}{\{0\}}$
  • D
    $(-\infty, \infty)$

Solution

Given, $f(x)=\frac{1}{\sqrt{|x|-x}}$ $f(x)$ is defined if $|x|-x>0$ $|x|>x$ It is possible only $x \in(-\infty, 0)$ $\therefore$ The domain of $f(x)$ is $(-\infty, 0)$.

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

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