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4. Let X an Y be sets with A, B C X and let f: X→Y be a function. Recall that {f(x) EYE A}, and f-¹(A) = {xe A: f(x) = A}. f(A) 1 (a) Show that A CS-¹(f(A)). (b) Give an example of a function f : X → Y and the set A such that f(f(A)) # A.

4. Let X an Y be sets with A, B C X and let f: X→Y be a function. Recall that {f(x) EYE A}, and f-¹(A) = {xe A: f(x) = A}. f(A) 1 (a) Show that A CS-¹(f(A)). (b) Give an example of a function f : X → Y and the set A such that f(f(A)) # A.

Advanced Engineering Mathematics
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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4. Let X an Y be sets with A, B C X and let f: X→Y be a function. Recall that f(A) = {f(x) EYE A), and f-¹(A) = {re A: f(x) = A}. (a) Show that A CS-¹(f(A)). (b) Give an example of a function f : X→ Y and the set A such that f(f(A)) ‡ A.
Transcribed Image Text:4. Let X an Y be sets with A, B C X and let f: X→Y be a function. Recall that f(A) = {f(x) EYE A), and f-¹(A) = {re A: f(x) = A}. (a) Show that A CS-¹(f(A)). (b) Give an example of a function f : X→ Y and the set A such that f(f(A)) ‡ A.
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