Question $2.(4+4=8$ points$)$ Suppose $f$:$R^{2}R$ is defined by $f(x,y)=|$~$x-y$~$|$ and $g$:$Q{R}^2$

is defined by $g(x)=(\frac{x}{2},\frac{-x}{2}).($Note that $|$~$.$~$|istheceilingfunction.$

$($a$)$ What is the image of $f?$ Prove your answer.