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Thread: (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 $\displaystyle x=2$

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

    Let $\displaystyle x=\frac{1}{2}$

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

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

    Adding (1) and (2),

    $\displaystyle 3f(2)=3$

    $\displaystyle f(2)=1$
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  3. #3
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    Smile

    Thanx
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