(27) Let f A → B and g : B → C be functions, and assume that their composition gof A→ C is one-to-one. Does this imply that both f and g are one-to-one? Prove your answer. (28) Let f A → B and g B → C be one-to-one functions, and assume that their composition g of A → C is onto. Does this imply that both f and g are onto? Prove your answer.
(27) Let f A → B and g : B → C be functions, and assume that their composition gof A→ C is one-to-one. Does this imply that both f and g are one-to-one? Prove your answer. (28) Let f A → B and g B → C be one-to-one functions, and assume that their composition g of A → C is onto. Does this imply that both f and g are onto? Prove your answer.
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter2: Functions
Section2.7: Combining Functions
Problem 4E
Related questions
Question
Transcribed Image Text:(27) Let f A → B and g B → C be functions, and assume that their composition
gof A→ C is one-to-one. Does this imply that both fand g are one-to-one?
Prove your answer.
(28) Let f : A → B and g : B C be one-to-one functions, and assume that their
composition go f : A → C is onto. Does this imply that both f and g are onto?
Prove your answer.
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