Counter examples to disprove mappings?

[xlalcciax]

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)

 

[micromass]

Yes, (a) is correct!

 

[xlalcciax]

Yes, (a) is correct!

Thanks!
Can You give me some clues for b) ?

 

[micromass]

Pick your favorite periodic function and transform it so that it is neither even nor odd...

 

[nicksauce]

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?

 

[xlalcciax]

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 ??

 

[SammyS]

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.