3. (1) Consider A = [0, 1] and B = [0, 1) and injections f(x) = x/3 from A to Band g(x) = x from B to A. Construct a bijection h from A to B such that on some points of A, h(x) = f(x), and for the other points of A, h(x) = g-'(x).
3. (1) Consider A = [0, 1] and B = [0, 1) and injections f(x) = x/3 from A to Band g(x) = x from B to A. Construct a bijection h from A to B such that on some points of A, h(x) = f(x), and for the other points of A, h(x) = g-'(x).
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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I cannot come up with good bijection! Could you help me with detailed explanation?
![3.
(1) Consider A = [0, 1] and B = [0, 1) and injections f(x) = x/3 from A to
Band g(x) = x from B to A. Construct a bijection h from A to B such that on some points
of A, h(x) = f(x), and for the other points of A, h(x) = g-'(x).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F56be79ad-be6a-45f1-b897-58d23fd7e62d%2F9210eae3-ddf2-4e9c-920d-a0118f9b2ed8%2Fqeh1xe.png&w=3840&q=75)
Transcribed Image Text:3.
(1) Consider A = [0, 1] and B = [0, 1) and injections f(x) = x/3 from A to
Band g(x) = x from B to A. Construct a bijection h from A to B such that on some points
of A, h(x) = f(x), and for the other points of A, h(x) = g-'(x).
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