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).
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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![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
Consider 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(An
B) = g¯¹(A) ng¯¹(B), and that g¯¹(AUB) = g¯¹(A) U g¯¹(B).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffa923b6f-81dd-482c-8885-6de6bc295751%2F45622f13-d1df-42a8-b622-0a511f5041e5%2Ffthjwon_processed.jpeg&w=3840&q=75)
Transcribed Image Text: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
Consider 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(An
B) = g¯¹(A) ng¯¹(B), and that g¯¹(AUB) = g¯¹(A) U g¯¹(B).
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