Can you do 44 pl 44. Suppose that ƒ : [a, b] → [a, b] is continuous. Prove that there is at least one fixed point in[a, b]-that is, x such that f(x) = X.45. If f: [a, b] →R is 1-1 and has the intermediate-value property-that is, if y is between f(u)and f(u), there is x between u and v such that f(x) = y-show that f is continuous. (Hint:First show that f is monotone.)Proveat there16tinuous function f RR such that, for each c ER, the equation●

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Answered: 44. Suppose that ƒ : [a, b] → [a, b] is…

44. Suppose that ƒ : [a, b] → [a, b] is continuous. Prove that there is at least one fixed point in [a, b]-that is, x such that f(x) = x. between f(u)

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter3: Functions

Section3.3: More On Functions; Piecewise-defined Functions

Problem 99E: Determine if the statemment is true or false. If the statement is false, then correct it and make it...

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Can you do 44 pl

44. Suppose that ƒ : [a, b] → [a, b] is continuous. Prove that there is at least one fixed point in
[a, b]-that is, x such that f(x) = X.
45. If f: [a, b] →R is 1-1 and has the intermediate-value property-that is, if y is between f(u)
and f(u), there is x between u and v such that f(x) = y-show that f is continuous. (Hint:
First show that f is monotone.)
Prove
at there
16
tinuous function f RR such that, for each c ER, the equation
●

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