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Let f: R → R be the function f(x) = 1². Provide an example of an open interval I such that f(1) is an open interval. Provide an example of an open interval J such that f-¹(J) is an open interval.

Let f: R → R be the function f(x) = 1². Provide an example of an open interval I such that f(1) is an open interval. Provide an example of an open interval J such that f-¹(J) is an open interval.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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I was thinking cosx and f(cosx), but I cannot really proove it. Please explain the correct answers please. Thank you!

Let f: R → R be the function f(x) = r². Provide an example of an open interval I such that f(I) is an open interval. Provide an example of an open interval J such that f-1(J) is an open interval.
Transcribed Image Text:Let f: R → R be the function f(x) = r². Provide an example of an open interval I such that f(I) is an open interval. Provide an example of an open interval J such that f-1(J) is an open interval.
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