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5. Let f: A B be a function. Define a relation on A by a₁ ~ƒ a₂ ⇒ f(a₁) = f(a₂) for all a₁, a2 € A. a. Show that ~f is an equivalence relation. b. If ƒ : R → R is defined by f(x) = sin(2x), find the equivalence class of 0 under this equivalence relation.

5. Let f: A B be a function. Define a relation on A by a₁ ~ƒ a₂ ⇒ f(a₁) = f(a₂) for all a₁, a2 € A. a. Show that ~f is an equivalence relation. b. If ƒ : R → R is defined by f(x) = sin(2x), find the equivalence class of 0 under this equivalence relation.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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5. Let f: A B be a function. Define a relation on A by a₁ ~ƒ a₂ ⇒ f(a₁) = f(a₂) for all a₁, a2 € A. a. Show that is an equivalence relation. b. If f: R→ R is defined by f(x) = sin(27x), find the equivalence class of 0 under this equivalence relation.
Transcribed Image Text:5. Let f: A B be a function. Define a relation on A by a₁ ~ƒ a₂ ⇒ f(a₁) = f(a₂) for all a₁, a2 € A. a. Show that is an equivalence relation. b. If f: R→ R is defined by f(x) = sin(27x), find the equivalence class of 0 under this equivalence relation.
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