# Even and Odd Function

A function $f(x)$ is *even* if
$f(−x)=f(x)$
A function $f(x)$ is *odd* if
$f(−x)=−f(x)$

Some extra facts about symmetric functions:

- EVEN x EVEN = EVEN
- ODD x ODD = EVEN
- EVEN x ODD = ODD

Example

$sin(x)$ is an odd function. $cos(x)$ is an even function.

From

Theorem

If $f$ is real then we can decompose it into even and odd functions as follows: $f_{even}(t)=2f(t)+f(−t) $ and $f_{odd}(t)=2f(t)−f(−t) $

$f(t)=f_{even}(t)+f_{odd}(t)$