2. a) Find an example of a real valued function f:R +R and SCR so that S is open while the forward image f(S) is closed. b) Find an example of a real valued function f :R →R and SCR so that S is closed while the forward image f(S) is open. This IS possible but this might be tougher; it's OK if you just provide a drawing of your example, even if you don't have the function precisely mathematically defined.
2. a) Find an example of a real valued function f:R +R and SCR so that S is open while the forward image f(S) is closed. b) Find an example of a real valued function f :R →R and SCR so that S is closed while the forward image f(S) is open. This IS possible but this might be tougher; it's OK if you just provide a drawing of your example, even if you don't have the function precisely mathematically defined.
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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Question
![2. a) Find an example of a real valued function f : R +R and SCR so that
S is open while the forward image f(S) is closed.
b) Find an example of a real valued function f : R →R and S C R so that S is
closed while the forward image f(S) is open. This IS possible but this might
be tougher; it's OK if you just provide a drawing of your example, even if you
don't have the function precisely mathematically defined.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F059f8a44-0099-41c0-92e3-ad75d014ebad%2F2b41309c-dc60-4ea2-afba-5d3b6f274369%2Fmggmo5m_processed.png&w=3840&q=75)
Transcribed Image Text:2. a) Find an example of a real valued function f : R +R and SCR so that
S is open while the forward image f(S) is closed.
b) Find an example of a real valued function f : R →R and S C R so that S is
closed while the forward image f(S) is open. This IS possible but this might
be tougher; it's OK if you just provide a drawing of your example, even if you
don't have the function precisely mathematically defined.
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