Question

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

• A. $(-\infty ,-1)\cup (2,\infty )$
• B. $[-1,1]\cup (2,\infty )\cup (-\infty ,-2)$
• C. $(-\infty ,1)\cup (2,\infty )$
• D. $[-1,1]\cup (2,\infty )$

Answer 1

The correct option is B $[-1,1]\cup (2,\infty )\cup (-\infty ,-2)$

$f\left(x\right)=\sqrt{\frac{1-|x|}{2-|x|}}\frac{1-|x|}{2-|x|}\ge 01-|x|\le 0\text{and}2-|x|<0\Rightarrow x\in [-1,1]$
Or,
$1-|x|\ge 0\text{and}2-|x|>0\Rightarrow x\in (\infty ,-2)\cup (2,\infty )$

Hence the domain will be,
$x\in [-1,1]\cup (-\infty ,-2)\cup (2,\infty )$