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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
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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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.
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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