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Math Help - Composition of Logarithmic Functions (f of g)

  1. #1
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    Question Composition of Logarithmic Functions (f of g)

    Find f of g and g of f if:

    f(x)= 1/(2x-1)
    g(x)=1-ln(x+1)

    How do I solve for x? Is this what I should do? How should I present my answers? Please help!

    f of g

    1/(2*1-ln(x+1)-1)

    1/(2-1-2ln(x+1))

    1/(1-ln(x+1)(x+1))

    x= -1

    g of f

    1-ln(1/(2x-1)+1)

    1-ln(2x/(2x-1))

    1=ln(2x/(2x-1))

    e1=2x/(2x-1)

    e(2x-1)=2x

    2xe-e=2x

    2xe-2x=e

    x(2e-2)=e

    x=e/(2e)

    x=1/2
    Last edited by SillyMath; June 16th 2012 at 11:37 PM.
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  2. #2
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    Re: Composition of Logarithmic Functions (f of g)

    You weren't asked to solve anything for x. Your answers for f of g and g of f are correct.
    Thanks from SillyMath
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  3. #3
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    Re: Composition of Logarithmic Functions (f of g)

    Thank you ^_^
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