Mapping/Composition/Definition

Composition

Let ${}L,\,M$ and ${}N$ denote sets, let

$F\colon L\longrightarrow M,x\longmapsto F(x),$

and

$G\colon M\longrightarrow N,y\longmapsto G(y),$

be mappings. Then the mapping

$G\circ F\colon L\longrightarrow N,x\longmapsto G(F(x)),$

is called the composition of the mappings ${}F$ and ${}G$.