Question

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

• A. $(-\infty ,\infty )-[-2,2]$
• B. $(-\infty ,\infty )-[-1,1]$
• C. $[-1,1]\cup (-\infty ,-2)\cup (2,\infty )$
• D. none of these

Answer 1

Answer: (C)

$[-1,1]\cup (-\infty ,-2)\cup (2,\infty )$

For given function to be defined, $\frac{1-|x|}{2-|x|}\ge 0$

$\Rightarrow \frac{|x|-1}{|x|-2}\ge 0$

$\Rightarrow |x|\in (-\infty ,1]\cup (2,\infty )\Rightarrow |x|\in [0,1]\cup (2,\infty )$, Since $|x|\ge 0$

$\Rightarrow x\in [-1,1]\cup (-\infty ,-2)\cup (2,\infty )$