U+2218 Ring Operator

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In mathematics, the composition operator $\circ$ takes two functions, $f$ and $g$, and returns a new function $h\left(x\right):=(g\circ f)\left(x\right)=g\left(f\right(x\left)\right)$. Thus, the function g is applied after applying f to x.

Reverse composition, sometimes denoted $f\mapsto g$ , applies the operation in the opposite order, applying $f$ first and $g$ second. Intuitively, reverse composition is a chaining process in which the output of function f feeds the input of function g.

The composition of functions is a special case of the composition of relations, sometimes also denoted by $\circ$. As a result, all properties of composition of relations are true of composition of functions, such as associativity.