Functions
Functions are fundamental to mathematics, and there is no doubt that you have been exposed to them before. However, I want to go over certain aspects of them in depth, as we will define things such as matrices as representations of functions later in the book.
The definition of a function
A function, for example, y = f(x), maps every element x in a set A to another element y in set B. Each element y is called the image of x under the function f(x). Set A is called the domain of the function and set B is called the codomain of the function. The domain and codomain of a function are denoted by f: A → B . The following mapping diagram shows the function f: X → Y.
Figure 3.5 – An example function [4]
All the images of f(x) form a set called the range. The range is a subset of the codomain. In the previous diagram of our function f: X → Y, the codomain was the set Y, but the range was the set {D, C}. The image of the...
