Theorem 10 Let f : [a, b] → R be a function of bounded variation on (a, b). If there exists a positive real number k such that 0 < k < f (x) for all x E [a, b}, then 1/f is a function of bounded variation on (a, b] and V(})
Theorem 10 Let f : [a, b] → R be a function of bounded variation on (a, b). If there exists a positive real number k such that 0 < k < f (x) for all x E [a, b}, then 1/f is a function of bounded variation on (a, b] and V(})
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.2: Mappings
Problem 27E: 27. Let , where and are nonempty. Prove that has the property that for every subset of if and...
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See the attachment. prove that
![Let f : [a, b] → R be a function of bounded variation
on [a, b]. If there exists a positive real number k such that 0 < k < f (x)
for all x € [a, b}, then 1/f is a function of bounded variation on [a, b] and
Theorem 10
た2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3703ae55-ef21-4668-a9c4-e55747f4d162%2F960f0ed1-d72f-4abf-bd64-4f3890c5ceb6%2Fqss5ic_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let f : [a, b] → R be a function of bounded variation
on [a, b]. If there exists a positive real number k such that 0 < k < f (x)
for all x € [a, b}, then 1/f is a function of bounded variation on [a, b] and
Theorem 10
た2
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