Decomposing a function into its even and odd parts

Re:Decomposing a function into its even and odd parts by mjd on Sunday July 31, 2016 @11:19AM (#12197321)

I think it's a little simpler to observe that

    fo1 - fo2 = fe1 - fe2

The left side is an odd function and the right side is an even function, so the common value must be both odd and even. But only the zero function is both odd and even, QED.

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Re:Decomposing a function into its even and odd parts by tamana on Sunday July 31, 2016 @11:45AM (#12197408)

Your don't even need to posit fe3 and fo2:

f(X) = e(X) + o(X)

f(-X) = e(X) - o(X)

From there you can explicitly solve the system of linear equations to get e(X) and o(X)

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