Question

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

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

Answer 1

The correct option is C $(0,1]$

By definition of $logx,x>0$ and also $lo{g}_{0.5}x\ge 0$
$\therefore x\le 1$ as in above question, base being less than 1;
domain is (0,1].