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 definition of a function

In mathematics, a function is a rule that assigns to each element of a set (called the domain) exactly one element of another set (called the codomain). It is typically represented by a mathematical equation or formula and is denoted by the symbol "f(x)" where "x" is a variable.

For example, a function that assigns to each real number x the value x^2 (x squared) is represented by the equation f(x) = x^2.

A function can also be defined as a process or a procedure that takes some input (or inputs), called the argument, and produces an output, called the value of the function.

For example, a function that takes an age and returns the corresponding category (child, teenager or adult)

Functions are important in mathematics and computer science, they are used to model and understand complex systems, to make predictions, and to solve problems.

It's important to note that, a function must be well defined, meaning that every element of the domain must have one and only one image in the codomain. Also, a function must not have any extraneous solutions.