 # Exercise 9.7.2. Let f : [0,1] [0,1] be a continuous function. Show...

## Question

Show transcribed text

## Transcribed Text

Exercise 9.7.2. Let f : [0,1] [0,1] be a continuous function. Show that there exists a real number x in [0,1] such that f(x) = x. (Hint: apply the intermediate value theorem to the function f(x) - x.) This point x is known as a fixed point of f, and this result is a basic example of a fixed point theorem, which play an important rôle in certain types of analysis. Theorem 9.7.1 (Intermediate value theorem). Let a < b, and let f : [a,b] R be a continuous function on [a,b]. Let y be a real number between f(a) and f (b), i.e., either f(a) < y < f (b) or f (a) >y > f (b) . Then there exists CE [a, b] such that f (c) = y.

## Solution Preview

These solutions may offer step-by-step problem-solving explanations or good writing examples that include modern styles of formatting and construction of bibliographies out of text citations and references. Students may use these solutions for personal skill-building and practice. Unethical use is strictly forbidden.

By purchasing this solution you'll be able to access the following files:
Solution.pdf.

\$3.00
for this solution

or FREE if you
register a new account!

PayPal, G Pay, ApplePay, Amazon Pay, and all major credit cards accepted.

### Find A Tutor

View available Advanced Math Tutors

Get College Homework Help.

Are you sure you don't want to upload any files?

Fast tutor response requires as much info as possible.