Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
(a) Assume that f: A onto B and g: B → A. Prove that g = f-¹ iff g of = IA or fog = IB (Theorem 4.4.4(b)).

(a) Assume that f: A onto B and g: B → A. Prove that g = f-¹ iff g of = IA or fog = IB (Theorem 4.4.4(b)).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question
### Transcription of Educational Text **(a)** Assume that \( f: A \xrightarrow{1-1 \ \text{onto}} B \) and \( g: B \rightarrow A \). Prove that \( g = f^{-1} \) if and only if \( g \circ f = I_A \) or \( f \circ g = I_B \) (Theorem 4.4.4(b)). **(b)** Give an example of sets \( A \) and \( B \) and functions \( f \) and \( g \) such that \( f: A \rightarrow B \), \( g: B \rightarrow A \), \( g \circ f = I_A \), and \( g \neq f^{-1} \).
Transcribed Image Text:### Transcription of Educational Text **(a)** Assume that \( f: A \xrightarrow{1-1 \ \text{onto}} B \) and \( g: B \rightarrow A \). Prove that \( g = f^{-1} \) if and only if \( g \circ f = I_A \) or \( f \circ g = I_B \) (Theorem 4.4.4(b)). **(b)** Give an example of sets \( A \) and \( B \) and functions \( f \) and \( g \) such that \( f: A \rightarrow B \), \( g: B \rightarrow A \), \( g \circ f = I_A \), and \( g \neq f^{-1} \).
Expert Solution
steps

Step by step

Solved in 2 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS