Let f: X→ Y and g: Y → V be functions. Show the following: (a) f is injective ↔h : Y→ X such that ho f = idr (b) f is surjective 3h: Y→ X such that foh = idy Use: ←

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.1: Inverse Functions
Problem 18E
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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
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)
Can you explain id x
Accessibility: Unavailable
Transcribed Image Text:On 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 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) Can you explain id x Accessibility: Unavailable
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