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Math Help - (x-1)f(x) + f(1/x) = 1

  1. #1
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    (x-1)f(x) + f(1/x) = 1

    The function f(x) satisfies the equation

    (x-1)f(x) + f(1/x) = 1 for all x not = 0.

    What is the value for f(2)?

    Thank you.
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  2. #2
    MHF Contributor alexmahone's Avatar
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    Let x=2

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

    Let x=\frac{1}{2}

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

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

    Adding (1) and (2),

    3f(2)=3

    f(2)=1
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  3. #3
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    Smile

    Thanx
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