Answer
False.
Work Step by Step
$g\left( x \right)={{\log }_{2}}x$
Consider the logarithmic function of the form ${{\log }_{a}}f\left( x \right)$, $f\left( x \right)>0$.
Here, $x>0$.
Therefore the domain of the function is $x>0$ that is, $\left( 0,\infty \right)$.
But it is stated that the domain is $\left[ 0,\infty \right)$.
Therefore, the statement is false.
