# Find range of  $f\left ( x \right )=\frac{1}{\left | x \right |-x}$  ; Option 1) $\left ( 0,\infty \right )$     Option 2) $\left [0,\infty \right )$ Option 3) $R$ Option 4) none of these.

As we learned

Range of function -

All possible values of  $f(x)\: \: \forall x\in$ domain  $(f)$ is known as Range

-

for $x> 0\: \: \: \: ;\: \: \: \left | x \right |=x$

for  $x< 0\: \: \: \: ;\: \: \: \left | x \right |=-x$

$f(x)=\frac{1}{-x-x}=\frac{-1}{2x}$

Option 1)

$\left ( 0,\infty \right )$

Option 2)

$\left [0,\infty \right )$

Option 3)

$R$

Option 4)

none of these.

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