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FunctionPeriod

FunctionPeriod[f,x] gives a period p of the function f over the reals such that f(x+p)f(x).

FunctionPeriod[f,x,dom] gives a period with x restricted to the domain dom.

FunctionPeriod[{f1,f2,…},{x1,x2,…},…] gives periods {p1,p2,…} for {x1,x2,…} such that f(x1+p1,x2+p2,…)f(x1,x2,…).

Please visit the official Wolfram Language Reference for more details and examples on core symbols.