Question

The domain of the function $\sqrt{\left({\log }_{0.5}x\right)}$ is

• A. $(1,\infty )$
• B. $(0,\infty )$
• C. $(0,1)$
• D. $(0.5,1)$

Answer 1

Answer: (C)

$(0,1)$

Let $f\left(x\right)=\sqrt{{\log }_{0.5}x}$

Firstly, $x>0$

And then, ${\log }_{0.5}x>0$

$\Rightarrow -{\log }_{2}x>0\Rightarrow {\log }_{2}x<0$

$\Rightarrow x<1$

$\therefore xϵ(0,1)$