H 22. Iff: X→ Y and g: Y→ Z are functions and g of is onto, must g be onto? Prove or give a counterexample.
H 22. Iff: X→ Y and g: Y→ Z are functions and g of is onto, must g be onto? Prove or give a counterexample.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
22
Transcribed Image Text:21. Hint: Suppose f: X→ Y and g: Y→ Z are func-
tions and g of is one-to-one. Given x₁ and x₂ in X, if
f(x₁) = f(x₂) then (g ° f)(x₁) = (gᵒf)(x₂). (Why?) Then
use the fact that g of is one-to-one.
Transcribed Image Text:H 22. Iff: X→ Y and g: Y→ Z are functions and
g of is onto, must g be onto? Prove or give a
counterexample.
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