H 21. Iff: X→ Y and g: Y→ Z are functions and g ofis one-to-one, must ƒ be one-to-one? Prove or givea counterexample. 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, iff(x₁) = f(x₂) then (g ° f)(x₁) = (g°f)(x₂). (Why?) Thenuse the fact that g of is one-to-one.

Let, for x, y ∈ X, f(x) = f(y) Then, g(f(x)) = g(f(y)) => g o f(x) = g o f(y)

Answered: H 21. Iff: X→ Y and g: Y→ Z are…

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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H 21. Iff: X→ Y and g: Y→ Z are functions and g of is one-to-one, must ƒ be one-to-one? Prove or give a counterexample.