IRL_ABooklet

Let $f:\mathbb{R}\to \mathbb{R}$ be the fractional part function, defined by $f(x)=x-\lfloor x\rfloor$, where $\lfloor x\rfloor$ is the greatest integer less than or equal to $x$. For instance, $f(5.4)=0.4$ and $f(-5.4)=0.6$. Let $g:\mathbb{R}\to \mathbb{R}$ be defined by $g(x)=f(1-2022x)$. Find 2023 distinct rational numbers $x$ satisfying $g(x)=x$. Each such solution $x$ should be explicitly written in the form $m/n$ for some integers $m,n$.