Let f be a one-to-one function from X=(1, 2, -, n) onto X. Let fk = fofo of denote the k-fold composition off with itself. Show that there are distinct positive integers i and j such that f'(x) = f(x) for all x EX. Show that for some positive integer k, f(x)=x for all Xx EX.
Let f be a one-to-one function from X=(1, 2, -, n) onto X. Let fk = fofo of denote the k-fold composition off with itself. Show that there are distinct positive integers i and j such that f'(x) = f(x) for all x EX. Show that for some positive integer k, f(x)=x for all Xx EX.
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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Discrete math question attached.
![Let f be a one-to-one function from X=(1, 2, -, n) onto X. Let fk = fofo of denote the k-fold composition off with itself. Show that there
are distinct positive integers i and j such that f'(x) = f(x) for all x EX. Show that for some positive integer k, f(x)=x for all Xx EX.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6e41cc9b-7a55-46c1-8b1f-6045ac18fd60%2F12983dfe-b15c-4066-930d-715c0284f5b6%2F9vei2n8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let f be a one-to-one function from X=(1, 2, -, n) onto X. Let fk = fofo of denote the k-fold composition off with itself. Show that there
are distinct positive integers i and j such that f'(x) = f(x) for all x EX. Show that for some positive integer k, f(x)=x for all Xx EX.
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