Function composition

In mathematics, the composition operator ∘ {\displaystyle \circ } takes two functions, f {\displaystyle f} and g {\displaystyle g} , and returns a new function f ∘ g {\displaystyle f\circ g} . When the composite function f ∘ g {\displaystyle f\circ g} (pronounced " f {\displaystyle f} of g {\displaystyle g} ") is evaluated at an input x {\displaystyle x} , the result is ( f ∘ g ) ( x ) = f ( g ( x ) ) {\displaystyle (f\circ g)(x)=f(g(x))} . That is, the function f {\displaystyle f} is applied after applying g {\displaystyle g} to x {\displaystyle x} . The composition of functions is a special case of the composition of relations, sometimes also denoted by ∘ {\displaystyle \circ } . As a result, all properties of composition of relations are true of composition of functions, such as associativity.