Even and odd functions

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. Even functions are those real functions whose graph is self-symmetric with respect to the y-axis, and odd functions are those whose graph is self-symmetric with respect to the origin. If the domain of a real function is self-symmetric with respect to the origin, then the function can be uniquely decomposed as the sum of an even function and an odd function.