Given a function f, defined as E in F, and a function g, defined as F in G, the composite of f and g is the function defined as E in G which applies all elements x of E on g(f(x)).
The result of the composition of two functions is called the composite of these two functions.
Symbol
The composite of the functions f and g (or f followed by g) is noted as g round g”).
Examples
Consider a function f defined by the relation f(x) = x² (represented here in purple) and a function g defined by the relation g(x) = sin(x) (represented here in green).
The composite g o f is defined by the relation g(f(x)) = sin(x²). Its graph is represented here in orange.
Consider a translation \(t\) of the drawing followed by a reflection \(s_d\) over axis \(d\) applied to a triangle ABC. The figure below shows \(\triangle{A^{\prime\prime}B^{\prime\prime}C^{\prime\prime}}\) that results from the composition of these two transformations :
\(\triangle{A^{\prime\prime}B^{\prime\prime}C^{\prime\prime}}=(s_d ∘ t)(\triangle{ABC})\)