Question

The domain of the function $f(x)=\sqrt{{\log }_2\left(\frac{1}{{\log }_{2}x}\right)}$ is given by

• A. $\{x:x>0\}$
• B. $\{x:0<x<1\}$
• C. $\{x:1<x\le 2\}$
• D. $\{x:x>1\}$

Answer 1

Answer: (C)

${\log }_2\left(\frac{1}{{\log }_{2}x}\right)\ge 0$ ]
$\frac{1}{{\log }_{2}x}\ge 1;\text{ also }{\log }_{2}x>0,x>1$
${\log }_{x}2\ge 1$
$2\ge x\Rightarrow x\le 2$
$\therefore 1<x\le 2\Rightarrow \text{ (3) }$