Problem

Source: ELMO Shortlist 2023 A4

Tags: Elmo, algebra



Let \(f:\mathbb R\to\mathbb R\) be a function such that for all real numbers \(x\neq1\), \[f(x-f(x))+f(x)=\frac{x^2-x+1}{x-1}.\]Find all possible values of \(f(2023)\). Proposed by Linus Tang