Problem 3 (Ex. 4.16). Suppose that ƒ : A → B and g : B → C are functions. (a) Prove that if g o f is injective then ƒ is injective. (b) Prove that if g of is surjective then g is surjective.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.5: Graphs Of Functions
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Problem 3 (Ex. 4.16). Suppose that f: A → B and g: B → C are functions.
(a) Prove that if g o f is injective then ƒ is injective.
(b) Prove that if g of is surjective then g is surjective.
Transcribed Image Text:Problem 3 (Ex. 4.16). Suppose that f: A → B and g: B → C are functions. (a) Prove that if g o f is injective then ƒ is injective. (b) Prove that if g of is surjective then g is surjective.
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