JEE MAIN - Mathematics (2011 - No. 4)
The domain of the function f(x) = $${1 \over {\sqrt {\left| x \right| - x} }}$$ is
$$\left( {0,\infty } \right)$$
$$\left( { - \infty ,0} \right)$$
$$\left( { - \infty ,\infty } \right) - \left\{ 0 \right\}$$
$$\left( { - \infty ,\infty } \right)$$
Paaiškinimas
$$f\left( x \right) = {1 \over {\sqrt {\left| x \right| - x} }},\,\,$$ define if $$\,\,\,\left| x \right| - x > 0$$
$$ \Rightarrow \left| x \right| > x,\,\,\, \Rightarrow x < 0$$
Hence domain of $$f\left( x \right)$$ is $$\left( { - \infty ,0} \right)$$
$$ \Rightarrow \left| x \right| > x,\,\,\, \Rightarrow x < 0$$
Hence domain of $$f\left( x \right)$$ is $$\left( { - \infty ,0} \right)$$