Can Trig Functions Satisfy These Conditions for Even and Odd Numbers?

  • Thread starter Thread starter mohamadh95
  • Start date Start date
  • Tags Tags
    Function
Click For Summary

Homework Help Overview

The discussion revolves around the exploration of functions that can differentiate between even and odd integers, specifically seeking functions h(x) and g(x) that meet certain criteria based on the parity of x.

Discussion Character

  • Exploratory, Conceptual clarification

Approaches and Questions Raised

  • Participants are considering the properties of functions that can yield specific outputs based on whether the input is even or odd. There are suggestions of using expressions involving powers of -1 and trigonometric functions.

Discussion Status

Some participants have proposed potential functions and expressions, while others are questioning the desired domain for these functions. The conversation is actively exploring different mathematical representations without reaching a consensus.

Contextual Notes

There is an emphasis on the domain of the functions, particularly whether it is restricted to integers or includes real numbers.

mohamadh95
Messages
43
Reaction score
0
is there any function h(x) that satisfies these conditions:
h(x)=0 when x is even
h(x)=1 when x is odd
and is there there any function g(x) such that:
g(x)=0 when x is odd
g(x)=1 when x is even
thank you.
 
Physics news on Phys.org
What's the desired domain? If it's only \mathbb{Z} think about the expression (-1)^x!
 
vanhees71 said:
What's the desired domain? If it's only \mathbb{Z} think about the expression (-1)^x!
Thank you for your quick reply g(x) can be (1+(-1)^x)/2 and h(x) (1-(-1)^x)/2
 
The trig functions are quite nice if the domain is ℝ. For example, look at cos2(pi*x) or cos(2*pi*x).
 

Similar threads

  • · Replies 7 ·
Replies
7
Views
2K
  • · Replies 8 ·
Replies
8
Views
2K
Replies
3
Views
2K
  • · Replies 12 ·
Replies
12
Views
1K
  • · Replies 11 ·
Replies
11
Views
3K
Replies
1
Views
2K
  • · Replies 3 ·
Replies
3
Views
2K
Replies
4
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 11 ·
Replies
11
Views
2K