Even and Odd Functions

From HvWiki

A function is defined as even iff f( - x) = f(x). Ie, if it is symmetrical about x = 0. A function is odd iff f( - x) = - f(x). It's possible for a function to be neither odd nor even.

Every sufficiently defined function is the sum of a odd part and an even part. For a function f(x):

E(x) = \frac{f(x) + f(-x)}{2}
O(x) = \frac{f(x) - f(-x)}{2}

A simple way to remember the definition of even and oddness is to remember that xn is even or odd as n is.

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