Let f: XY and g: Y→ V be functions. Show the following: (a) f is injective 3h: Y→X such that ho f = idx (b) f is surjective 3h : Y→ X such that fo h= idy Use: v injective if x1 ‡xn → v(x1) = v(xn) How to prove these <-> How to proof with the arrows <-> (do you prove both rhs and lhs)

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Please teach how to solve not just solve (concepts)
Let f: X→ Y and g: Y→ V be functions. Show the following:
3h: Y→X such that ho f = id₂
(a) f is injective
(b) f is surjective
3h: Y→X such that fo h = idy
Use:
v injective if x1 ‡xn → v(x1) = v(xn)
#
How to prove these <-> How to proof with the arrows <-> (do you prove both rhs and lhs)
Transcribed Image Text:Please teach how to solve not just solve (concepts) Let f: X→ Y and g: Y→ V be functions. Show the following: 3h: Y→X such that ho f = id₂ (a) f is injective (b) f is surjective 3h: Y→X such that fo h = idy Use: v injective if x1 ‡xn → v(x1) = v(xn) # How to prove these <-> How to proof with the arrows <-> (do you prove both rhs and lhs)
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