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Hi again, here is my problem and my efforts

  1. Jan 9, 2004 #1
    i wish i could find a solution for that poblem

    it is about inverse function:
    Show that the function has an inverse function, and find [(d/dx)f^-1(x))] x=a for the given number a

    f(x)=e^3x + 2e^x - 5 , x>=0 , a=-2

    Here i proved that the function has an inverse by finding f'(x), and found that it is increasing at the given interval.

    then f(x)= -2 to find "x", and then substitute in the theory:
    g(a)=1/[f'(g(a))]

    the problem here is that i can't find "x"
    where, e^3x + 2e^x - 3 = 0

    please i need help, any efforts will be appreciated
     
  2. jcsd
  3. Jan 9, 2004 #2
    [tex]f(x) = e^{3x} + 2e^x - 5[/tex]

    to find, f^-1(x), change x to y. find y.

    [tex]x = e^{3y} + 2e^y - 5[/tex]
    [tex]lnx = 3y + ln 2e^y - ln5[/tex]
    [tex]lnx = 4y + ln 0.4[/tex]
    [tex]ln 2.5x = 4y[/tex]
    [tex]y = ln2.5x/4[/tex]

    [tex]y = f^{-1}(x)[/tex]
    [tex]y' = 1/(10x) [/tex]
     
  4. Jan 10, 2004 #3
    hey PrudensOptimus What are u doing. These properties of ln are not in the league
     
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