Question 79
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 $m, n$.
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 $m, n$.