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# f(x) function returns an output after processing

Construct a function and it returns a value. In design, some objects, or spaces, may have functions. They have a set of rules which determine their outcome. Whatever input goes into them, the outcome is determined by a specific process. It is very deterministic.

It’s worth looking at cell functions also

## PHP Function

In the website language ‘php’:

`<?php`

function foo($arg_1, $arg_2, /* ..., */ $arg_n)

{

echo "Example function.n";

return $retval;

}

?>

## Mathematical Functions

Functions, in a mathematical sense, express the idea that one quantity (the argument of the function, also known as the input) completely determines another quantity (the value, or the output). Functions assign exactly one value to each input of a specified type. The argument and the value may be real numbers, but they can also be elements from any given sets: the domain and the codomain of the function. An example, with the real numbers as both its domain and codomain is the function f(x) = 2x, which assigns to every real number the real number with twice its value. In this case, it is written that f(5) = 10.

In addition to elementary functions on numbers, functions include maps between algebraic structures like groups and maps between geometric objects like manifolds. In the abstract set-theoretic approach, a function is a relation between the domain and the codomain that associates each element in the domain with exactly one element in the codomain. An example of a function with domain {A,B,C} and codomain {1,2,3} associates A with 1, B with 2, and C with 3.

There are many ways to describe or represent functions: by a formula, by an algorithm that computes it, by a plot or a graph. A table of values is a common way to specify functions in statistics, physics, chemistry, and other sciences. Functions may also be described through their relationship to other functions, for example, as the inverse function or a solution of a differential equation.

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