Mapping/Image under a mapping/Definition

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

${\displaystyle F\colon L\longrightarrow M}$

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

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

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

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

is called the image of the mapping.