Question

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

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

Answer 1

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

Given,

$f\left(x\right)=\frac{\sqrt{2+x}+\sqrt{2-x}}{x}$

For $f\left(x\right)$ to be defined

$x\ne 0$
$2+x\ge 0\Rightarrow x\ge -2$
$2-x\ge 0\Rightarrow x\le 2$
$\therefore x\in [-2,0)\cup (0,2]$