Question

The domain of the fuction $f\left(x\right)=\sqrt{{\log }_{16}{x}^2}$ is ?

• A. $x=0$
• B. $|x|\ge 4$
• C. $|x|\ge 1$
• D. $|x|\ge 2$

Answer 1

The correct option is C $|x|\ge 1$

$Given$
$f\left(x\right)=\sqrt{{\log }_{16}{x}^2}$
$The\text{domain of a funcion is the set of input or argument values}$
$\text{for which the function is real and defined}$
${\log }_{16}{x}^2\ge 0$
$\Rightarrow x^2\ge {16}^0$
$\Rightarrow x^2\ge 1$
$\Rightarrow x^2-1\ge 0$
$\Rightarrow (x-1)(x+1)\ge 0$
$x\ge 1orx\le 1$
$(-\propto ,1]\cup [1,\propto )$
$Hence$
$Domain:\left|x\right|\ge 1$