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  4. The domain of the function y=(1/√|x|-x) is:

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Q. The domain of the function $ y=\frac{1}{\sqrt{|x|-x}} $ is:

Jharkhand CECEJharkhand CECE 2003

Solution:

Given, $y=\frac{1}{\sqrt{|x|-x}}$
When $x \geq 0 \,\,y=\frac{1}{\sqrt{x-x}}=\infty$ (not defined)
When $x < 0 \,\,y=\frac{1}{\sqrt{-x-x}}=\frac{1}{\sqrt{-2 x}} $
$\therefore $ Given function is defined for every negative values of $x$ .
$ \therefore $ Required domain is $(-\infty, 0)$.