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Let f : [0, 1] → [0, 1] and f be continuous on [0, 1]. Show that there exists x E [0, 1] such that f(x) = = x. Hir

Let f : [0, 1] → [0, 1] and f be continuous on [0, 1]. Show that there exists x E [0, 1] such that f(x) = = x. Hir

Advanced Engineering Mathematics
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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Let f : [0, 1] → [0, 1] and f be continuous on [0, 1]. Show that there exists x E [0, 1] such that f(x) = x. Hint: construct an appropriate continuous function and use the Intermediate Value Property.
Transcribed Image Text:Let f : [0, 1] → [0, 1] and f be continuous on [0, 1]. Show that there exists x E [0, 1] such that f(x) = x. Hint: construct an appropriate continuous function and use the Intermediate Value Property.
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