function (mathematics)

In mathematics, a function f is a non-empty set of ordered pairs (x, f(x)) of which no two can have the same first element. Hence, if f(x) = x² two ordered pairs are (-2,4) and (2,4). The set of all first elements in a function's ordered pairs is called the domain; the set of all second elements is the range. Functions are used in all branches of mathematics, physics, and science generally. For example, in the equation y = 2x + 1, y is a function of the symbol x. This can be written as y = f(x).

In another example, the formula t = 2π√(l/g) shows that for a simple pendulum, the time of swing t is a function of its length l and of no other variable quantity (π and g, the acceleration due to gravity, are constants).