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I have a problem: g(x) is an even periodic function with ${T} > {0}$. Show that there exists ${c}$ with ${0<c<T}$ such that $${g}(c+x)={g}(c−x)$$for every real number {x}.

james
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nyz
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  • this is linked to my previous question: https://math.stackexchange.com/questions/3538758/show-that-2a-b-is-a-period-of-f – nyz Feb 08 '20 at 07:24

1 Answers1

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If $c=\frac{T}{2}$ then

$$ g(c+x)=g(c+x-2c)=g(x-c)\overset{\text{ g is even}}{=}g(c-x) $$

Jo Jomax
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