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A fixed point theorem Suppose that a function ƒ is
Chapter 2, Problem 67E(choose chapter or problem)
QUESTION:
Problem 67E
A fixed point theorem Suppose that a function ƒ is continuous on the closed interval [0, 1] and that 0 ≤ ƒ(x) ≤ 1 for every x in [0, 1]. Show that there must exist a number c in [0, 1] such that ƒ(c) = c (c is called a fixed point of ƒ).
Questions & Answers
QUESTION:
Problem 67E
A fixed point theorem Suppose that a function ƒ is continuous on the closed interval [0, 1] and that 0 ≤ ƒ(x) ≤ 1 for every x in [0, 1]. Show that there must exist a number c in [0, 1] such that ƒ(c) = c (c is called a fixed point of ƒ).
ANSWER:
Solution:-
Step 1 of 2
Given that
We have to show that there must exist a number c in [0, 1] such that ƒ(c) = c (c is called a fixed point of ƒ).