Answered: Suppose f [a, b] → [a, b] is…

Suppose f [a, b] → [a, b] is continuous. Prove there exists c € [a, b] such that f(c) = c. (Hint: Consider the function g(x) = f(x) = x.) -

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter1: Functions

Section1.3: Properties Of Functions

Problem 1E

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Suppose f [a, b] → [a, b] is continuous. Prove there exists c [a, b] such that f(c) = c.
(Hint: Consider the function g(x) = f(x) - x.)

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