2) Suppose f:X→Y and g: Y→ Z are functions and gof is 1-1. ) Must f always be 1-1? Explain why or give a counterexample. ) [from Example 7.3.19] Must g always be 1-1? punterexample. Prove or give a
2) Suppose f:X→Y and g: Y→ Z are functions and gof is 1-1. ) Must f always be 1-1? Explain why or give a counterexample. ) [from Example 7.3.19] Must g always be 1-1? punterexample. Prove or give a
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![**(12)** Suppose \( f: X \rightarrow Y \) and \( g: Y \rightarrow Z \) are functions and \( g \circ f \) is 1-1.
**(a)** Must \( f \) always be 1-1? Explain why or give a counterexample.
**(b)** [from Example 7.3.19] Must \( g \) always be 1-1? Prove or give a counterexample.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F34a6820a-e392-4bc6-a071-8d3939523d24%2Fdc6e6f94-3a9b-4b01-8ed5-9dad3d0eb6ae%2Fg7oij5b_processed.png&w=3840&q=75)
Transcribed Image Text:**(12)** Suppose \( f: X \rightarrow Y \) and \( g: Y \rightarrow Z \) are functions and \( g \circ f \) is 1-1.
**(a)** Must \( f \) always be 1-1? Explain why or give a counterexample.
**(b)** [from Example 7.3.19] Must \( g \) always be 1-1? Prove or give a counterexample.
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