Problem #PRU-65921

Problems Algebra Functional equations Calculus Functions of one variable. Continuity Periodicity and aperiodicity

Problem

The function \(f (x)\) is defined for all real numbers, and for any \(x\) the equalities \(f (x + 2) = f (2 - x)\) and \(f (x + 7) = f (7 - x)\) are satisfied. Prove that \(f (x)\) is a periodic function.