Mapping/Composition/Definition

Composition

Let $L,M$ and $N$ denote sets, let

$F:L⟶M,x⟼F(x),$

and

$G:M⟶N,y⟼G(y),$

be mappings. Then the mapping

$G\circ F:L⟶N,x⟼G(F(x)),$

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