Suppose f : [a, b] → [a, b] is continuous. Prove there exists c E [a, b] such that f(c) = c.
Suppose f : [a, b] → [a, b] is continuous. Prove there exists c E [a, b] such that f(c) = c.
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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![Suppose f : [a, b] → [a, b] is continuous. Prove there exists c E [a, b] such that f(c) =
(Hint: Consider the function g(x) = f(x) – x.)
= C.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa5a7bb65-b92b-4b2a-a8a3-c52d52b3b98d%2F0eb6ab0e-4d40-4127-9e51-3f5fcb5be298%2Fhcrv4of_processed.png&w=3840&q=75)
Transcribed Image Text:Suppose f : [a, b] → [a, b] is continuous. Prove there exists c E [a, b] such that f(c) =
(Hint: Consider the function g(x) = f(x) – x.)
= C.
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