Question

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

(1) $(-\infty, \infty)$

(2) $(0, \infty)$

(3) $(-\infty, 0)$

(4) $(-\infty, \infty)-\{0\}$

Answer 1

$f(x)=\frac{1}{\sqrt{|x|-x}} \Rightarrow|x|-x>0 \Rightarrow|x|>x \quad \Rightarrow \quad x<0$ $\therefore \quad x \in(-\infty, 0)$ Ans.

Above Correct Answer is Option (3)