Let a\gt 0 be a real number and f(x) a real function defined on all of \mathbb{R}, satisfying for all x\in\mathbb{R},</p>


a) Prove that the function f is periodic; i.e., there exists b\gt 0 such that for all x, f(x+b)=f(x).

b) Give an example of such a nonconstant function for a=1.

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