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Let f: (0,3] →→→R such that f(x) = 1². • Show that f(r) < 1. • Show that f has no fixed point on (0,3]. Hint: Assume there were f(c) = c and derive a contradiction. • Show that the function f(x) = 1 from [0, ∞) to [0, ∞) has a fixed point c. Hint: Set f(x) = x = and show the resulting equation has a solution in [0, 00) using the the IVP.

Let f: (0,3] →→→R such that f(x) = 1². • Show that f(r) < 1. • Show that f has no fixed point on (0,3]. Hint: Assume there were f(c) = c and derive a contradiction. • Show that the function f(x) = 1 from [0, ∞) to [0, ∞) has a fixed point c. Hint: Set f(x) = x = and show the resulting equation has a solution in [0, 00) using the the IVP.

Linear Algebra: A Modern Introduction
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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10.1. #2 A,B,C. Thanks. 

2. Let f : (0, ] –→ R such that f(x) = r². Show that f(x) < z. Show that f has no fixed point on (0, 3]. Hint: Assume there were f(c) = c and derive a contradiction. Show that the function f(x) = from [0, ∞0) to [0, 0) has a fixed point c. Hint: Set f(x) = x and show the resulting equation has a solution in [0, 00) using the the IVP.
Transcribed Image Text:2. Let f : (0, ] –→ R such that f(x) = r². Show that f(x) < z. Show that f has no fixed point on (0, 3]. Hint: Assume there were f(c) = c and derive a contradiction. Show that the function f(x) = from [0, ∞0) to [0, 0) has a fixed point c. Hint: Set f(x) = x and show the resulting equation has a solution in [0, 00) using the the IVP.
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