## Notes Information

Login / Sign Up to View Document

## Sample Document Text

Functions. A mapping. Usual notation If a ∈ A , f ( a ) = b ∧ b ∈ B f: A → B
a b c A B d y x m z
All members of A are mapped to the set B. A is the domain of the function f, B, its range or codomain. Functions as relations. Composite functions. f: A→B and then g: B→C is a mapping g*f such that g*f: A → C.
One-to-0ne, Onto function A function f: A → B is one-to-one if all its members are mapped, and different members of A are mapped to different members in B. Also called injective functions. A function is onto if all elements of B are images of some elements of A. a m o n p An onto function is also called a surjective function. A function that is both one-to-one and onto are called bijective functions or a one-to-one correspondence. General features of one-to-one and onto functions For an one-to-one f: A → B we cannot have distinct pairs (a,b), (c,b). b c
No horizontal line can intersect f at more than one points. For an onto function, ∀b ∈ B , ∃a ∈ A such that ( a , b ) belongs...

© Copyright 2020 , Koofers, Inc. All rights reserved.

The information provided on this site is protected by U.S. and International copyright law, and other applicable intellectual property laws, including laws covering data access and data compilations. This information is provided exclusively for the personal and academic use of students, instructors and other university personnel. Use of this information for any commercial purpose, or by any commercial entity, is expressly prohibited. This information may not, under any circumstances, be copied, modified, reused, or incorporated into any derivative works or compilations, without the prior written approval of Koofers, Inc.