4. Let f: R R to be a contiuous, strictly monotone function. Let f(R) = R. Thus its the inverse f-1 is defined on the whole real line R. Show that f-1: R R continous on R.
4. Let f: R R to be a contiuous, strictly monotone function. Let f(R) = R. Thus its the inverse f-1 is defined on the whole real line R. Show that f-1: R R continous on R.
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter3: The Derivative
Section3.CR: Chapter 3 Review
Problem 6CR
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![4. Let f: R R to be a contiuous, strictly monotone function. Let f (R) = R.
Thus its the inverse f-1 is defined on the whole real line R. Show that f-1: R R
continous on R.
Hint: note Theorem 2.10 only deals with the case where the domain is a closed,
bounded interval. So you cannot apply it directly to problem 4. But you may follow
the proof of continuity of g(a) = V: [0, 00) [0, 00), which was considered as the
inverse of f(x) = : (0, 00) (0, 00).
1.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe6dba997-101e-43e2-95cb-d4dc7d29171d%2F587163e9-002c-4192-b424-b555dd89f140%2F24trkbk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:4. Let f: R R to be a contiuous, strictly monotone function. Let f (R) = R.
Thus its the inverse f-1 is defined on the whole real line R. Show that f-1: R R
continous on R.
Hint: note Theorem 2.10 only deals with the case where the domain is a closed,
bounded interval. So you cannot apply it directly to problem 4. But you may follow
the proof of continuity of g(a) = V: [0, 00) [0, 00), which was considered as the
inverse of f(x) = : (0, 00) (0, 00).
1.
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