# The domain of the function$\dpi{100} f(x)=\frac{1}{\sqrt{\left | x \right |-x}}is$ Option 1) $(-\infty ,0)\;$ Option 2) $\; (-\infty,\infty)-\left \{ 0 \right \}\;$ Option 3) $\; \; (-\infty,\infty)\;$ Option 4) $\; (0,\infty)$

As we learnt in

DOMAIN -

The domain of R is the set of all first elements of the ordered pairs in a relation R.

- wherein

eg. R={(a,b),(c,d)}, then domain is {a,c}

$f(x)=\frac{1}{\sqrt{|x|-x}}$,                 |x| - x > 0

x < |x|  it is only for -ve number. So that $n\epsilon(-\infty, 0)$

Correct option is 1.

Option 1)

$(-\infty ,0)\;$

This is the correct option.

Option 2)

$\; (-\infty,\infty)-\left \{ 0 \right \}\;$

This is an incorrect option.

Option 3)

$\; \; (-\infty,\infty)\;$

This is an incorrect option.

Option 4)

$\; (0,\infty)$

This is an incorrect option.

N

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