Question

$f\left(x\right)=\frac{1}{{(\left|x\right|-x)}^{1/2}}$. Then the domain of the function is

• A. $x>0$
• B. $x\ge 0$
• C. $x<0$
• D. $x\le 0$

Answer 1

Answer: (C)

$x<0$

For real values of $y$,

$|x|-x>0$ and $|x|-x\ne 0$

For $x>0$

$|x|-x=x-x$

$=0$

Thus for all $x>0$, $|x|-x=0$.

For $x<0$

$|x|-x$$=-x-x$$=-2x$

Since $x<0$

$-2x>0$

Thus domain of $f\left(x\right)$ is
$x<0$.