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When referring to applying g(x) to f(x), the function composition is denoted as (f\:\circ\:g)(x),\:or\:f(g(x)). Functions. A function basically relates an input to an output, thereâs an input, a relationship and an output. For every input there is only one output.
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 a special case of the composition of relations, so all properties of the latter are true of composition of functions. The composition of function has some additional properties.