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Math Help - Need help on proofs

  1. #1
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    Need help on proofs

    Suppose all you know about a function f is that f(ab)= f(a) + f(b), A(upsidedown) a, b greater than 0.
    Find f(1).
    Here's a picture of it. It's part c. Thanks.
    http://pic90.picturetrail.com/VOL237.../389570493.jpg
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  2. #2
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    Quote Originally Posted by rowdy3 View Post
    Suppose all you know about a function f is that f(ab)= f(a) + f(b), A(upsidedown) a, b greater than 0.
    Find f(1).
    Here's a picture of it. It's part c. Thanks.
    http://pic90.picturetrail.com/VOL237.../389570493.jpg
    f(1) = f(1 \cdot 1) = f(1) + f(1) = 2f(1)

    so ... if f(1) = 2f(1) , what must f(1) equal?
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  3. #3
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    1=1*1, so
    f(1)=f(1*1)
    f(1*1)+f(1)+f(1)
    f(1)=2f(1)
    therefore, f(1)=0
    f(x^2) = f(x*x) = f(x)+f(x) = 2f(x)
    let y = sqrt(x)
    f(x) = f(y*y) = f(y) + f(y)
    therefore f(y) = f(x)/2
    Last edited by rowdy3; July 12th 2010 at 07:05 PM.
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