Given any two periodic functions, \(\color{red}{f(x)}\) and \(\color{blue}{g(x)}\), the function \(\color{purple}{h(x)} = \color{red}{f(x)} + \color{blue}{g(x)}\) will also be periodic with a period that is, at most, the product of the original two periods (the period of \(f(x)\) times the period of \(g(x)\)).

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