Answer
False.
Work Step by Step
Assume the domain of $f$ consists of all real numbers $x \geq 2$. Therefore, $x = 3$ should produce a real result. However, $f(3)=\sqrt(2-3)=\sqrt(-1)$, which isn't real. Thus, $x=3$ isn't part of the domain. However, $3\geq2$. Thus, the assumption (the statement) must be false.