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Searching for a function

  1. Sep 18, 2013 #1
    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.
     
  2. jcsd
  3. Sep 18, 2013 #2

    vanhees71

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    2016 Award

    What's the desired domain? If it's only [itex]\mathbb{Z}[/itex] think about the expression [itex](-1)^x[/itex]!
     
  4. Sep 18, 2013 #3
    Thank you for your quick reply g(x) can be (1+(-1)^x)/2 and h(x) (1-(-1)^x)/2
     
  5. Sep 18, 2013 #4

    D H

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    Staff Emeritus
    Science Advisor

    The trig functions are quite nice if the domain is ℝ. For example, look at cos2(pi*x) or cos(2*pi*x).
     
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