A Functional Equation Hunt

★ 9/10functions Substitution algebra Functional Equations

Problem

Find all functions $f \colon \mathbb{R} \to \mathbb{R}$ satisfying

f(f(x+y)) = f(x+y) + f(x)f(y) - xy \qquad \text{for all } x, y \in \mathbb{R}.

Answer

Solution

Difficulty	9/10
Topics	functions, Substitution, algebra, Functional Equations

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