A fixed point theorem Suppose that a function ƒ is

Chapter 2, Problem 67E

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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).

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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).

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