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Let f: X→ Y and g: Y→ V be functions. Show the following: (a) fis injective 3h: Y→ X such that ho f = idx (b) f is surjective 3h : Y→ X such that fo h = idy =

Let f: X→ Y and g: Y→ V be functions. Show the following: (a) fis injective 3h: Y→ X such that ho f = idx (b) f is surjective 3h : Y→ X such that fo h = idy =

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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Let f X Y and g: Y→ V be functions. Show the following: (a) f is injective h: Y→ X such that hof= idx (b) f is surjective ⇒h : Y→ X such that fo h = idy Use: v injective if x1 ‡xn → v(x1) ‡ v(xn)
Transcribed Image Text:Let f X Y and g: Y→ V be functions. Show the following: (a) f is injective h: Y→ X such that hof= idx (b) f is surjective ⇒h : Y→ X such that fo h = idy Use: v injective if x1 ‡xn → v(x1) ‡ v(xn)
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