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Counter examples to disprove mappings?

  • Thread starter xlalcciax
  • Start date
  • #1
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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)
 

Answers and Replies

  • #2
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Yes, (a) is correct!
 
  • #3
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Yes, (a) is correct!
Thanks!
Can You give me some clues for b) ?
 
  • #4
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Pick your favorite periodic function and transform it so that it is neither even nor odd...
 
  • #5
nicksauce
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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?
 
  • #6
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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 ??
 
  • #7
SammyS
Staff Emeritus
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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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