Question

The domain of $f\left(x\right)=\sqrt{\left|x\right|-x}$ is

• A. $(-\infty ,0)$
• B. $(0,\infty )$
• C. $(-\infty ,\infty )$
• D. $(0,1)$

Answer 1

The correct option is C $(-\infty ,\infty )$

function is defined when $|x|-x⩾0$
$\Rightarrow |x|⩾x$
$|x|⩾x\forall x\in R$
$\therefore f$ is defined every where in $R$