Function (mathematics)

In mathematics, a function^[1] is a relation atween a set o inputs an a set o permissible ootputs wi the property that ilka input is relatit tae exactly ane ootput. An example is the function that relates ilka real nummer x tae its square x². The ootput o a function f correspondin tae an input x is denotit bi f(x) (reid "f o x"). In this example, if the input is −3, then the ootput is 9, an we mey write f(−3) = 9. The input variable(s) are sometimes referred tae as the argument(s) o the function.

A function f taks an input x, an returns an ootput f(x). Ane metaphor describes the function as a "machine" or "black box" that for each input returns a correspondin ootput.