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sum of a linear and periodic funtion

Source: Bundeswettbewerb 2003, Second Stage, problem 1

January 17, 2004
functiongeometrygeometric transformationrotationalgebra solvedalgebra

Problem Statement

The graph of a function f:Rā†’Rf: \mathbb{R}\to\mathbb{R} has two has at least two centres of symmetry. Prove that ff can be represented as sum of a linear and periodic funtion.
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