Algebra · Linear functions · Function composition · Polynomial identity
Problem 4, 2022
Let \(f\) and \(g\) be linear functions with the following three properties: the graph of \(x \mapsto f(g(x))\) passes through the point \((2021, 2022)\), the graph of \(x \mapsto g(f(x))\) passes through the point \((2022, 2021)\), and
\[ f(g(x)) - g(f(x)) = 2 \qquad \text{for every real number } x. \]
Determine the value of \(f(2021) - g(2022)\).
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Serbian Municipal Competition 2022, high school grade I, category A, problem 4. Organized by the Mathematical Society of Serbia (DMS). Source