MAT 1348 Study Guide - Final Guide: Surjective Function, Bijection, Identity Function

• School: University of Ottawa
• Department: Mathematics
• Course: MAT 1348
• Professor: Guy Beaulieu

Document Summary

Defns: a function f from a set a to a set b is a rule that assigns each element of a to exactly one element in b. A is called the domain of f , b is called the codomain of f . For an element a a, f (a) is the image of a. (note that f (a) b. ) The subset of b that contains all elements that are images of some a a is called the image of a. Similarly we can de ne the image of a subset s of a. The image of s a is {f (a) : a s}. The preimage f 1(b) of an element b b is de ned as f 1(b) = {a a : f (a) = b}. Defns: a function f : a b is one-to-one (also called an injection) if f (x) = f (y) x = y for all x, y a.