MathDB
function as sum of a linear function and a periodic function

Source: Turkey TST 2002 - P4

April 6, 2013
functionsymmetryalgebra proposedalgebra

Problem Statement

If a function ff defined on all real numbers has at least two centers of symmetry, show that this function can be written as sum of a linear function and a periodic function.
[For every real number xx, if there is a real number aa such that f(aāˆ’x)+f(a+x)=2f(a)f(a-x) + f(a+x) =2f(a), the point (a,f(a))(a,f(a)) is called a center of symmetry of the function ff.]