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f(10+x) = f(10- x) and f(20+x) = - f(20- x), odd and periodic wanted

Source: 1997 ITAMO p2

January 25, 2020
oddfunctionperiodicperiodic functionalgebra

Problem Statement

Let a real function ff defined on the real numbers satisfy the following conditions: (i) f(10+x)=f(10−x)f(10+x) = f(10- x) (ii) f(20+x)=−f(20−x)f(20+x) = - f(20- x) for all xx. Prove that f is odd and periodic.
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