4. Let X an Y be sets with A, B C X and let f: X→Y be a function. Recall thatf(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.

Answered: Image /qna-images/answer/6ad77ff4-62c0-4b3b-9595-1d8661da85f3.jpg

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.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.5: The Kernel And Range Of A Linear Transformation

Problem 30EQ

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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.

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