Question

The domain of $f\left(x\right)=\frac{1}{\sqrt{x+2}}+\frac{1}{\sqrt{2-x}}+\frac{1}{x}$ is

• A. $(-2,2)$
• B. $(-2,0)\cup (0,2)$
• C. $(0,\infty )$
• D. $(-\infty ,0)$

Answer 1

The correct option is B $(-2,0)\cup (0,2)$

$f$ is defined if denominators are not equal to zero and terms under square root exist.
$\Rightarrow x+2>02-x>0x\ne 0$
$\Rightarrow x>-2x<2$
$\therefore$ $f$ is defined on $(-2,2)-\left\{0\right\}$.
$=(-2,0)\cup (0,2)$