Elementary questions about functions, notation, properties, and operations such as function composition.
In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output.
A function is defined by its set of inputs, called the domain; a set containing the set of outputs, and possibly additional elements, as members, called its codomain ; and the set of all input-output pairs, called its graph. Sometimes the codomain is called the function's range, but more commonly the word "range" is used to mean, instead, specifically the set of outputs (also called the image of the function). For example, we could define a function using the rule $f(x) = x^2$ by saying that the domain and codomain are the real numbers, and that the graph consists of all pairs of real numbers $(x, x^2)$.