Question
The domain of the function $$f\left( x \right) = \frac{1}{{\sqrt {\left| x \right| - x} }}$$ is
A.
$$\left( {0,\infty } \right)$$
B.
$$\left( { - \infty ,0} \right)$$
C.
$$\left( { - \infty ,\infty } \right) - \left\{ 0 \right\}$$
D.
$$\left( { - \infty ,\infty } \right)$$
Answer :
$$\left( { - \infty ,0} \right)$$
Solution :
$$\eqalign{
& f\left( x \right) = \frac{1}{{\sqrt {\left| x \right| - x} }},{\text{define}}\,{\text{if}}\,\left| x \right| - x > 0 \cr
& \Rightarrow \left| x \right| > x, \Rightarrow x < 0 \cr} $$
Hence domain of $$f\left( x \right)$$ is $$\left( { - \infty ,0} \right)$$