2. Suppose f : X →Y and g : Y → Z are functions, and g of :X → Z is injective. (a) Show that f is injective. (b) Provide an example where f is not injective. (c) Impose a condition on f so that it, together with the assumption that gof is injective, implies that g is injective.

2. Suppose f : X →Y and g : Y → Z are functions, and g of :X → Z is injective. (a) Show that f is injective. (b) Provide an example where f is not injective. (c) Impose a condition on f so that it, together with the assumption that gof is injective, implies that g is injective.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter8: Polynomials

Section8.3: Factorization In F [x]

Problem 25E

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2. Suppose f : X →Y and g : Y → Z are functions, and g of :X → Z is injective.
(a) Show that f is injective.
(b) Provide an example where f is not injective.
(c) Impose a condition on f so that it, together with the assumption that gof is injective, implies that
g is injective.

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