It is proved that any function defined on a symmetric interval can be uniquely expressed as the sum of an even function and an odd function

It is proved that any function defined on a symmetric interval can be uniquely expressed as the sum of an even function and an odd function

Let f (x) be your arbitrary function. Existence proof: G (x) = [f (x) + F (- x)] / 2, H (x) = [f (x) - f (- x)] / 2, easy to test, the above two functions are even function and odd function respectively, and f (x) = g (x) + H (x). Uniqueness proof: Let f (x) = G1 (x) + H1 (x), (...)

Elden Ring Premiere

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