# R to R/Even and odd function/Definition

Even function

A
function
is called * even*, if for all
the identity

holds.

A function
is called * odd*, if for all
the identity

holds.

Even function

A
function
${}f\colon \mathbb {R} \rightarrow \mathbb {R}$
is called * even*, if for all
${}x\in \mathbb {R}$
the identity

- ${}f(x)=f(-x)\,$

holds.

A function
${}f\colon \mathbb {R} \rightarrow \mathbb {R}$
is called * odd*, if for all
${}x\in \mathbb {R}$
the identity

- ${}f(x)=-f(-x)\,$

holds.