Let $f(x)$ be a function defined on $\mathbb{R}$. If for every real number $x$, the relationships $$f(x+3)\le f(x)+3\quad\text{and}\quad f(x+2)\ge f(x)+2$$ always hold. 1) Show $g(x) = f(x)-x$ is a periodic function. 2) If $f(998)=1002$, compute $f(2000)$