Answered: Let f : X → Y and g : Y → Z be…

Let f : X → Y and g : Y → Z be functions such that h = go ƒ is a one-to-one correspondence. (a) Prove that f is one-to-one. (b) Prove that g is onto.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.3: Properties Of Composite Mappings (optional)

Problem 12E: Let f:AB and g:BA. Prove that f is one-to-one and onto if fg is one to-one and gf onto.

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Question

*35.
Let f : X → Y and g : Y → Z be functions such that h = g o ƒ is a one-to-one
correspondence.
(a) Prove that f is one-to-one.
(b) Prove that g is onto.

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