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*) = *x*² (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(*x*²). 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 :

\(\triangle{A^{\prime\prime}B^{\prime\prime}C^{\prime\prime}}=(s_d ∘ t)(\triangle{ABC})\)