# Composition of Functions

## Composition of Functions

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