Odd function

Definition

An odd function is a function $f$ defined on a subset of the reals satisfying the following two conditions:

1. The domain of the function is symmetric about 0, i.e., for every $x$ in the domain, $-x$ is also in the domain.
2. For every $x$ in the domain, we have the following condition:

$\!f(-x)=-f(x)$

Related notions

• Even function
• Even part
• Odd part