Answer
False.
Work Step by Step
Assume $f(x)=g(x)$ for all $x$. Therefore, $f(2)$ should equal $g(2)$. $f(2)=|2|=2$ and $g(2)=-|2|=-2$. However, $2\ne-2$. Therefore, $f(x) \ne g(x)$ at $x=2$. $2$ is a part of the real numbers, so by counterexample, the statement is false.
