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a) Explain why the function f(x) = e#² is not injective (one-to-one) on its natural domain.

a) Explain why the function f(x) = e#² is not injective (one-to-one) on its natural domain.

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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(a) Explain why the function f(x) = e² is not injective (one-to-one) on its natural domain. (b) Find the largest possible domain A, where all elements of A are non-negative and f: A → R, f(x) = e"² is injective. (c) Find a codomain B such that f: A → B, f(x) = e is surjective. (d) Show that g: B → A, g(x) = VIn x is the inverse of f. Why is f"(x) # -VIn x?
Transcribed Image Text:(a) Explain why the function f(x) = e² is not injective (one-to-one) on its natural domain. (b) Find the largest possible domain A, where all elements of A are non-negative and f: A → R, f(x) = e"² is injective. (c) Find a codomain B such that f: A → B, f(x) = e is surjective. (d) Show that g: B → A, g(x) = VIn x is the inverse of f. Why is f"(x) # -VIn x?
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