Mapping/Image under a mapping/Definition

Image of a map

Let ${}L$ and ${}M$ be sets, and let

$F\colon L\longrightarrow M$

be a mapping. For a subset ${}S\subseteq L$, we call

${}F(S)={\left\{y\in M\mid {\text{there exists an }}x\in S{\text{ such that }}F(x)=y\right\}}\,$

the image of ${}S$ under ${}F$. For ${}S=L$,

${}F(L)=\operatorname {Im} F\,$

is called the image of the mapping.