Even and odd functions

Functions such that f(–x) equals f(x) or –f(x)

In mathematics, an even function is a real function such that f ( − x) = f ( x) {\displaystyle f(-x)=f(x)} for every x {\displaystyle x} in its domain. Similarly, an odd function is a function such that f ( − x) = − f ( x) {\displaystyle f(-x)=-f(x)} for every x {\displaystyle x} in its domain. They are named for the parity of the powers of the power functions which satisfy each condition: the function f ( x) = x n {\displaystyle f(x)=x^{n}} is even if n is an even integer, and it is odd if n is an odd integer.

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