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Math Help - Period : 2

  1. #1
    Super Member dhiab's Avatar
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    Period : 2

    Find the period for the function f in R:
    f(x+1)f(x)+f(x+1)+1=f(x)
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  2. #2
    MHF Contributor red_dog's Avatar
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    We have f(x+1)=\frac{f(x)-1}{f(x)+1}.

    Replace x with x+1:

    f(x+2)=\frac{f(x+1)-1}{f(x+1)+1}=\frac{\displaystyle\frac{f(x)-1}{f(x)+1}-1}{\displaystyle\frac{f(x)-1}{f(x)+1}+1}=-\frac{1}{f(x)}

    Replace x with x+2:

    f(x+4)=-\frac{1}{f(x+2)}=-\frac{1}{\displaystyle -\frac{1}{f(x)}}=f(x).

    Then the period is 4.
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