R to R/Even and odd function/Definition

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.