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Math Help - inverse function

  1. #1
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    inverse function

    If f(x)=2x+ln x, find f^{-1}(2).
    I keep getting stuck trying to get the inverse. Here's what i got:
    y=2x+lnx
    -e^{lnx}+e^y=e^{2x}
    -x+e^y=e^{2x}
    Then i don't know what to do, and i feel like i'm approaching it incorrectly.
    So, i tried: \frac{y}{2x}=lnx
    x=e^{\frac{y}{2x}} and i'm still not getting anywhere.
    Any help would be mucho appriciated!
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by windir View Post
    If f(x)=2x+ln x, find f^{-1}(2).
    I keep getting stuck trying to get the inverse. Here's what i got:
    y=2x+lnx
    \color{red}-e^{lnx}+e^y=e^{2x}
    -x+e^y=e^{2x}
    Then i don't know what to do, and i feel like i'm approaching it incorrectly.
    So, i tried: \frac{y}{2x}=lnx
    x=e^{\frac{y}{2x}} and i'm still not getting anywhere.
    Any help would be mucho appriciated!
    by inspection, f^{-1}(2) = 1 since f(1) = 2(1) + \ln 1 = 2 + 0 = 2


    (by the way, what you did is incorrect. from the line in red)
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  3. #3
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    ah thank you! obvious stuff usually trips me up!
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by windir View Post
    ah thank you! obvious stuff usually trips me up!
    you'd be surprised how common this vice is. take care.
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