Question

# The domain of the function $f(x) = \dfrac{1}{{\sqrt {\left| x \right| - x} }}$ is$A.( - \infty ,\infty ) \\ B.(0,\infty ) \\ C.( - \infty ,0) \\ D.( - \infty , - \infty ) - \{ 0\} \\$

Hint:This is a simple question based on function and its domain set and codomain set. As we know that domain is the set of all the values that go into a function. We will find the set of possible values which will satisfy the given function.

$f(x) = \dfrac{1}{{\sqrt {\left| x \right| - x} }}$
It means, $\sqrt {\left| x \right| - x} > 0 \\ \\$
Which further shows that, $\left| x \right| - x > 0$
$\Rightarrow \left| x \right| > x$
Thus, the domain of function will be $( - \infty ,0)$. Here the set must be open on both sides.