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Homework Help: Natural Logs and composition

  1. Feb 10, 2010 #1
    1. The problem statement, all variables and given/known data
    I keep getting what I think is the "right answer", but it's not one of my choices :^(
    Here are the problems and answer choices.
    1).
    precal1.jpg
    2).
    precal2.jpg

    2. Relevant equations

    nothing really...or at least I don't think besides the fact that e^-x = 1/e^x

    3. The attempt at a solution

    1).
    x + 14 = 2 g^( - 1) ( x )
    (x + 14) / 2 = g^( - 1) ( x)

    x - 3 = 4 f^( - 1) ( x)
    ( x - 3) / 4 = f^( - 1) ( x)

    g^( - 1) o f^( - 1) ( x) = (x + 53) / 8
    I get this for number 1, but it is not one of the answer choices!

    2).
    6 = 7e^x + e^(-x )
    Let e^x = t, (t > 0), thus e^(-x) = 1/t
    6 = 7t + 1/t
    Multiplying each side by t
    6t = 7t² + 1
    7t² - 6t + 1 = 0
    t = (3 ± √2)/7
    e^x = t ==> x = ln (t)
    x = ln [(3 + √2)/7] or x = ln [(3 − √2)/7]
    I get this for number 2, but it is also not one of the answer choices!
     
  2. jcsd
  3. Feb 10, 2010 #2

    LCKurtz

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    Science Advisor
    Homework Helper
    Gold Member

    I agree with both your answers.
     
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