The domain of the function

Question:

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

Solution:

$f(x)=\frac{1}{\sqrt{|x|-x}}$

f(x) is defined if |x| − x > 0

i.e |x| > x

i.e x < |x

which is possible for negative real numbers

$\therefore$ Domain for $f(x)$ is $\mid R^{-} \sim\{0\}$

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