Counter examples to disprove mappings?

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Homework Help Overview

The discussion revolves around counterexamples aimed at disproving certain statements regarding real-valued functions, specifically focusing on odd, even, monotonic, and periodic functions.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants are attempting to identify counterexamples for three statements regarding functions. They discuss specific functions like sinh(x) and consider transformations such as phase shifts to explore the properties of periodic functions.

Discussion Status

Some participants have confirmed the correctness of the first statement regarding odd functions and are seeking further guidance for the second and third statements. Suggestions have been made to consider specific transformations of periodic functions and the implications of shifting functions.

Contextual Notes

Participants are exploring the implications of function properties under transformations, with an emphasis on the definitions of odd, even, monotonic, and periodic functions. There is a focus on finding counterexamples that challenge the initial statements without reaching a consensus on the outcomes.

xlalcciax
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give counter examples to disprove the following statements:
a) a real valued odd function cannot be strictly monotonic
b) a real valued periodic function must be odd or even
c) a real valued monotonic function cannot be even


a) sinh(x) ??
b)
c)
 
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Yes, (a) is correct!
 
micromass said:
Yes, (a) is correct!

Thanks!
Can You give me some clues for b) ?
 
Pick your favorite periodic function and transform it so that it is neither even nor odd...
 
xlalcciax said:
Thanks!
Can You give me some clues for b) ?

Think of a periodic function that is odd or even. Now phase shift it slightly. Is it still odd or even?
 
nicksauce said:
Think of a periodic function that is odd or even. Now phase shift it slightly. Is it still odd or even?


yeah. i have got it now!
what about c) ? f(x)=2 ??
 
xlalcciax said:
Thanks!
Can You give me some clues for b) ?
Any odd function which is continuous on (−∞, +∞), passes through the origin.

Take an odd periodic function & shift it up or down.
 

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