Exercise 4.5.8 (Inverse functions). If a function f: AR is one-to-one, then we can define the inverse function f-1 on the range of f in the natural way: f¹(y)=x where y = f(x). Show that if f is continuous on an interval [a, b] and one-to-one, then f-1 is also continuous.
Exercise 4.5.8 (Inverse functions). If a function f: AR is one-to-one, then we can define the inverse function f-1 on the range of f in the natural way: f¹(y)=x where y = f(x). Show that if f is continuous on an interval [a, b] and one-to-one, then f-1 is also continuous.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.5: Rational Functions
Problem 48E
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![Exercise 4.5.8 (Inverse functions). If a function f: AR is one-to-one,
then we can define the inverse function f-1 on the range of f in the natural
way: f¹(y)=x where y = f(x).
Show that if f is continuous on an interval [a, b] and one-to-one, then f-1 is
also continuous.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc6389447-1237-4af0-b5c6-eb1260425b55%2F0d32f0ca-7584-45f2-a54e-3b85643f3685%2Fi2qxbsf_processed.png&w=3840&q=75)
Transcribed Image Text:Exercise 4.5.8 (Inverse functions). If a function f: AR is one-to-one,
then we can define the inverse function f-1 on the range of f in the natural
way: f¹(y)=x where y = f(x).
Show that if f is continuous on an interval [a, b] and one-to-one, then f-1 is
also continuous.
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