Skip to Main Content
The Nuts and Bolts of Proofs, 4th Edition
book

The Nuts and Bolts of Proofs, 4th Edition

by Antonella Cupillari
January 2011
Beginner content levelBeginner
296 pages
11h 43m
English
Academic Press
Content preview from The Nuts and Bolts of Proofs, 4th Edition
10. Let f : ℝ→(1, +)andg:(1,+) →ℝbe defined as f ( x)=x
2
+ 1 and gðyÞ= y 1
p
: Then f and g
are inverse functions of each other.
11. Let f : A B be a function. If f has an inverse function, then f is a bijection. (This is the converse of
the statement in Example 4.2.16.)
A Little More about Functions and Sets
The definition of function relies on sets like the domai n, the codomain, and the range. So it is not surprising
to conjecture that there might be a lot of important relations between functions, sets, and their operations.
We will examine some of them.
Again, let f be a function between the sets A and B, f : A B. The range of f is the subset ...
Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
and much more.
Start your free trial

You might also like

Discrete Structures, Logic, and Computability, 4th Edition

Discrete Structures, Logic, and Computability, 4th Edition

James L. Hein

Publisher Resources

ISBN: 9780123822178