在数学领域，两个函数的复合函数指一个将第一个函数作用于参数，然后再将第二个函数作用于所得结果的函数。

具体来说，给定两个函数f : X → Y和g : Y → Z，其中f的陪域等于g的定义域（称为f、g可复合），则其复合函数，记为g o f，以X为定义域，Z为陪域，并将任意x∈X映射为g(f(x))。有时也省略复合记号“o”，直接写作g f。

函数的复合满足结合律：若f、g可复合，g、h可复合，则有：

函数的复合可以看作是二元关系复合的一个特例。

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 f : X → Y and g : Y → Z can be composed to yield a function which maps x in X to g(f(x)) in Z. Intuitively, if z is a function of y, and y is a function of x, then z is a function of x. The resulting composite function is denoted g ∘ f : X → Z, defined by (g ∘ f )(x) = g(f(x)) for all x in X. The notation g ∘ f is read as "g circle f ", or "g round f ", or "g composed with f ", "g after f ", "g following f ", or "g of f", or "g on f ". Intuitively, composing two functions is a chaining process in which the output of the inner function becomes the input of the outer function.