f: X→Y and g: Y→V be bijective functions. Show the following: ) gof: X→V is injective. ) gof: X→ Vis surjective. (gof)¹ = f¹ og ¹ Use: v injective if x1 xn → v(x1) = v(xn) ‡ ‡
f: X→Y and g: Y→V be bijective functions. Show the following: ) gof: X→V is injective. ) gof: X→ Vis surjective. (gof)¹ = f¹ og ¹ Use: v injective if x1 xn → v(x1) = v(xn) ‡ ‡
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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Transcribed Image Text:f: X→Y and g: Y→V be bijective functions. Show the following:
) gof: X→V is injective.
) gof: X→ Vis surjective.
(gof)¹ = f¹ og ¹
Use:
v injective if x1 xn → v(x1) = v(xn)
‡
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