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Function

In mathematics, a function connects the argument of the function which is referred to as the input and the value of the function is referred to as the output. Exactly, one output is assigned by a function for each input. The values can be any kind of real numbers and in addition to it, the values can also be the elements from any of the given set. A good example for a function is f(x) = 2x where a function will eventually associate with each number twice as large the number like the number "five" will be associated with number “ten” then in the f(x) formula it will be written as f(5) = 10.

There are no specifications that the input to the function should certainly be a number. Even the input can be a well defined object. For instance, a function can even associate the letter A with the number “one” and the letter B with the number "two" and similarly with any other letter. A function can be described in various ways like in the form of an algorithm or formula and where the output for the given input will be computed. It can also be described in the form of a graph which depicts the picture of the function or it can even be depicted in the form of a table of values which gives the output for particular inputs. Engineering, science and statistics do follow a common table of values.

Domain:

Domain is the name given to the set of all the inputs to a particular set of function. The functions are usually defined to have a codomain which is mainly associated with some fixed set which has got all the possible outputs like the codomain of the real valued functions which contains all the real numbers though every real number is not included in a particular real valued function. The inputs and the outputs (x,f(x)) of a particular function of all the ordered pairs is called its graph.

All outputs of a specific function are referred to as its image. Some texts use the word range in order to refer to the image while others have a codomain.

Function Composition:

There are two or more functions that take the output where one or more functions will be the input of others. By applying f to the argument x and obtaining y= f (x) and applying g to y and obtaining z = g (y).

A composite function can be written with f and g as,

g º f : x → Z

x → g(f(x))

Questions:

• What is a function?
• What is a Domain?
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