Function (mathematics)

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A function is a very important thing in mathematics. It is a rule that tells you what to do to an object in order to get a different object.

Functions are usually written as f(x). The f is short for function. f(x) is said: "function of x" or "f (eff) of x", for short.

It is sometimes said that f(x) is the image of x, and x is the pre-image of f(x). Also, it is said that the object x is transformed or mapped into f(x).

[edit] Example

Here is an example of how functions work:
f(x) = x + 1 is a formula for a function. You are doing something to x that will make it a different number. In this example, you are adding 1 to the unknown number x. If you set x = 4, the function becomes f(4) = 4 + 1. This means that f(x) = 5 when x equals 4.

Many functions are more complex than this example but the pattern is always the same. For every input, x, you get a result, f(x).

[edit] Types of functions

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There are other functions, like trigonometric functions. In mathematical language, a function can be defined as a map from a non-empty set (called a domain) to a non-empty set (called a co-domain) such that for every element in the domain there is a corresponding unique element in the co-domain.

There are several basics types of functions:

  • constant functions: all elements in the domain go to some fixed element in the co-domain
  • injective functions: any two different elements are transformed into different ones
  • surjective functions: all elements in the co-domain have a pre-image
  • bijective functions: if it is both injective and surjective