Let DCR and let f: D→ R be afunction. For a set B CR the preimage of B under ƒ is f−¹(B) = {x €D | ƒ(x) ¤ B}. [This is just notation, f−¹ is not considered to be afunction here, and in fact f-¹ may not exist as a function.]1Consider the function ƒ : R → R given by f(x) = x². Let A = [0, 2][1,1]. Find f-¹(A) and f-1(B). Does f-¹(An B)f-¹(A)nf-¹(B)? Does f-¹(AUB) = f¹(A) Uf-¹(B)?and B ==Let g: RR be a function, and let A, B C R. Prove that g-¹(AnB) = g¯¹(A) ng¯¹(B), and that g¯¹(AUB) = g¯¹(A) U g¯¹(B).

Answered: Image /qna-images/answer/45622f13-d1df-42a8-b622-0a511f5041e5.jpg

Let DCR and let f: D→ R be a function. For a set B CR the preimage of B under ƒ is f−¹(B) = {x € D | ƒ(x) ¤ B}. [This is just notation, f-¹ is not considered to be a function here, and in fact f-¹ may not exist as a function.] 1 1 Consider the function fƒ : R → R given by f(x) = x². Let A = [0, 2] [1,1]. Find f-¹(A) and f-1(B). Does f-¹(An B) f-¹(A)nf-¹(B)? Does f-¹(AUB) = f¹(A) Uf-¹(B)? and B = = Let g: RR be a function, and let A, B CR. Prove that g-¹ (An B) = g¯¹(A) ng¯¹(B), and that g¯-¹(AUB) = g¯¹(A) U g¯¹(B).

Let DCR and let f: D→ R be a function. For a set B CR the preimage of B under ƒ is f−¹(B) = {x € D | ƒ(x) ¤ B}. [This is just notation, f-¹ is not considered to be a function here, and in fact f-¹ may not exist as a function.] 1 1 Consider the function fƒ : R → R given by f(x) = x². Let A = [0, 2] [1,1]. Find f-¹(A) and f-1(B). Does f-¹(An B) f-¹(A)nf-¹(B)? Does f-¹(AUB) = f¹(A) Uf-¹(B)? and B = = Let g: RR be a function, and let A, B CR. Prove that g-¹ (An B) = g¯¹(A) ng¯¹(B), and that g¯-¹(AUB) = g¯¹(A) U g¯¹(B).

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.4: Definition Of Function

Problem 63E

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