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.
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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