(d) Suppose that ƒ: P → Q and g: Q → R are functions. (i) Show that the composite function gof : P → R is bijective if both ƒ and g are bijective. (ii) If gof is bijective, show that (gof)−¹ = f−¹og¯¹.
(d) Suppose that ƒ: P → Q and g: Q → R are functions. (i) Show that the composite function gof : P → R is bijective if both ƒ and g are bijective. (ii) If gof is bijective, show that (gof)−¹ = f−¹og¯¹.
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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![(d) Suppose that ƒ: P → Q and g: Q→ R are functions.
(i) Show that the composite function gof: P→ R is bijective if both f and g are
bijective.
(ii) If gof is bijective, show that (gof)-¹ = f-¹og-¹.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbcd41a60-1c57-48e5-af3c-1aa1a8fd7e84%2F8ba0afee-6ec1-4a25-8c45-be398a42cb5e%2Fvcwxtpe_processed.png&w=3840&q=75)
Transcribed Image Text:(d) Suppose that ƒ: P → Q and g: Q→ R are functions.
(i) Show that the composite function gof: P→ R is bijective if both f and g are
bijective.
(ii) If gof is bijective, show that (gof)-¹ = f-¹og-¹.
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