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: $f_{even}(t)=\frac{f(t)+f(-t)}{2}$ and $f_{odd}(t)=\frac{f(t)-f(-t)}{2}$

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