Find a codomain B such that ƒ: A → B, ƒ(x) = e²´ is surjective. Show that g: B → A, g(x) = Vln x is the inverse of f. Why is f-(x) # -VIn x?
Find a codomain B such that ƒ: A → B, ƒ(x) = e²´ is surjective. Show that g: B → A, g(x) = Vln x is the inverse of f. Why is f-(x) # -VIn x?
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter5: Rings, Integral Domains, And Fields
Section5.4: Ordered Integral Domains
Problem 8E: If x and y are elements of an ordered integral domain D, prove the following inequalities. a....
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Questions C and D
Transcribed Image Text:(a) Explain why the function f(x) = e=° 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** is injective.
(c) Find a codomain B such that f: A→ B, f(x) = e*² is surjective.
(d) Show that g: B → A, g(x) = Vln x is the inverse of f. Why is f-'(x) # -VIn x?
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