Appendix B Functions

If A and B are sets, then a function f from A to B, written f: AB, is a rule that associates to each element x in A a unique element denoted f(x) in B. The element f(x) is called the image of x (under f), and x is called a preimage of f(x) (under f). If f: AB, then A is called the domain of f, B is called the codomain of f, and the set {f(x): xA} is called the range of f. Note that the range of f is a subset of B. If SA, we denote by f(S) the set {f(x): xS} of all images of elements of S. Likewise, if TB, we denote by f1(T) the set {xA: f(x)T} of all preimages of elements in T. Finally, two functions f: AB and g: AB are equal, written f=g, if f(x)=g(x) for all xA.

Example 1

Suppose that A=[10, 10]. Let f: A

Get Linear Algebra, 5th Edition now with O’Reilly online learning.

O’Reilly members experience live online training, plus books, videos, and digital content from 200+ publishers.