Question

The complete solution set of the inequation $\frac{1}{|lo{g}_{1/2}|x||}>1$ is

• A. $(-2,-\frac{1}{2})U(\frac{1}{2},1)U(1,2)$
• B. $(-\infty ,0)U(0,\infty )$
• C. $(-2,-1)U(-1,-\frac{1}{2})U(\frac{1}{2},1)U(1,2)$
• D. $(-2,-\frac{1}{2})U(\frac{1}{2},2)$

Answer 1

Answer: (C)

$(-2,-1)U(-1,-\frac{1}{2})U(\frac{1}{2},1)U(1,2)$

The complete solution set.........................

$|x|>0,|x|\ne 1$

$\Rightarrow x\ne 1,-10$

$xϵ(-\infty ,-1)\cup (-1,0)\cup (0,1)\cup (1,\infty ).........\left(1\right)$

$|lo{g}_{1/2}|X||<1$

$-1<lo{g}_{1/2}|x|<1$

$\frac{1}{2}<|x|<2$

$\Rightarrow xϵ(-2,-\frac{1}{2})\cup (\frac{1}{2},2)..........\left(2\right)$

$\left(1\right)\cup \left(2\right)$ gives

$xϵ(-2,-1)\cup (-1,-\frac{1}{2})\cup (\frac{1}{2},1)\cup (1,2)$