Let A, B and C be nonempty sets and let f : A → B, g: BC and h: B → C be functions. For each of the following, prove or disprove: (a) If f is bijective and go f = hof, then g = h. (b) If gof=hof, then g = h.

Let A, B and C be nonempty sets and let f : A → B, g: BC and h: B → C be functions. For each of the following, prove or disprove: (a) If f is bijective and go f = hof, then g = h. (b) If gof=hof, then g = h.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.4: Definition Of Function

Problem 55E

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Let A, B and C be nonempty sets and let f : A → B, g: BC and h: B → C be functions.
For each of the following, prove or disprove:
(a) If f is bijective and gof= hof, then g = h.
(b) If gof= hof, then g = h.

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