Counter examples to disprove mappings?

  • Thread starter xlalcciax
  • Start date
  • #1
12
0
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
22,089
3,297
Yes, (a) is correct!
 
  • #3
12
0
Yes, (a) is correct!

Thanks!
Can You give me some clues for b) ?
 
  • #4
22,089
3,297
Pick your favorite periodic function and transform it so that it is neither even nor odd...
 
  • #5
nicksauce
Science Advisor
Homework Helper
1,272
5
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
12
0
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
Science Advisor
Homework Helper
Gold Member
11,368
1,035
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.
 

Related Threads on Counter examples to disprove mappings?

Replies
9
Views
2K
  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
1
Views
973
Replies
10
Views
2K
Replies
6
Views
973
  • Last Post
Replies
7
Views
2K
Replies
4
Views
880
Replies
6
Views
4K
Replies
8
Views
5K
Replies
1
Views
973
Top