Question

The domain of $f\left(x\right)=\sqrt{{\log }_{2}x}-{\log }_2\sqrt{x}$ is

• A. $x>0$
• B. $x\ge 1$
• C. $x>1$
• D. $x\ge 2$

Answer 1

The correct option is B $x\ge 1$

$f\left(x\right)=\sqrt{{\log }_{2}x}-{\log }_2\sqrt{x}$
For $f\left(x\right)$ to be defined,
${\log }_{2}x\ge 0$ and $\sqrt{x}>0$
$\Rightarrow x\ge 1$ and $x>0$
$\Rightarrow x\ge 1$