In mathematics, function composition is the pointwise application of one function to the result of another to produce a third function. For instance, the functions and can be composed to yield a function which maps in to in . Intuitively, if is a function of , and is a function of , then is a function of . The resulting composite function is denoted , defined by for all in . The notation is read as ” circle “, or ” round “, or ” composed with “, ” after “, ” following “, or ” of “. Intuitively, composing two functions is a chaining process in which the output of the first function becomes the input of the second function. The composition of functions is just a particularization of the composition of relations, so all properties of the latter operation also transfer to the composition of functions. The composition of function has some additional properties however.