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f: X→Y and g: Y→V be bijective functions. Show the following: ) gof: X→ V is injective. ) gof: X → V is surjective. ) (gof)-¹-f¹og-¹

f: X→Y and g: Y→V be bijective functions. Show the following: ) gof: X→ V is injective. ) gof: X → V is surjective. ) (gof)-¹-f¹og-¹

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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f: X→ Y and g: Y→V be bijective functions. Show the following: ) gof: X → V is injective. ) gof: X → V is surjective. ) (gof)-¹=f-¹og=¹ Use: v injective if x1 ‡xn → v(x1) = v(xn)
Transcribed Image Text:f: X→ Y and g: Y→V be bijective functions. Show the following: ) gof: X → V is injective. ) gof: X → V is surjective. ) (gof)-¹=f-¹og=¹ Use: v injective if x1 ‡xn → v(x1) = v(xn)
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