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    I'm so confused: the book says the inverse of e^x is lnx....ok I know this is obviously correct....but surely if y = e^x, then the inverse should be Iny ???? Please help



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    you got it horribly wrong.
    -e^ln(x) = x
    -if y = e^x, x = ln y
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    (Original post by anoymous1111)
    I'm so confused: the book says the inverse of e^x is lnx....ok I know this is obviously correct....but surely if y = e^x, then the inverse should be Iny ???? Please help



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    An inverse function is a reflection in the line y=x. For this reason, when you say that

    y=e^x \Rightarrow x = \ln y

    you need to swap x and y to get the correct inverse function (as a function of x).
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    (Original post by shawn_o1)
    you got it horribly wrong.
    -e^ln(x) = x
    -if y = e^x, x = ln y
    Isn't the second bit what I said? oh god I just don't get it at all


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    (Original post by Indeterminate)
    An inverse function is a reflection in the line y=x. For this reason, when you say that

    y=e^x \Rightarrow x = \ln y

    you need to swap x and y to get the correct inverse function (as a function of x).
    Ahhhh ok that makes sense! Im just missing the whole point!


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    (Original post by anoymous1111)
    Ahhhh ok that makes sense! Im just missing the whole point!


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    Kind of like how you say the inverse of x^2 is \sqrt{x} not \sqrt{y}. (for the nitpickers, assume a suitably picked domain to make x^2 injective.)
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    (Original post by Zacken)
    Kind of like how you say the inverse of x^2 is \sqrt{x} not \sqrt{y}. (for the nitpickers, assume a suitably picked domain to make x^2 injective.)
    Ah god I don't know how the hell I misunderstood so much! Thank you!!!


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    (Original post by anoymous1111)
    Ah god I don't know how the hell I misunderstood so much! Thank you!!!


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    Don't fret it, it's better than you come on here and make an effort to understand it. I admire that! Most people simply shrug and don't bother trying to understand. :-)
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    (Original post by Zacken)
    Don't fret it, it's better than you come on here and make an effort to understand it. I admire that! Most people simply shrug and don't bother trying to understand. :-)
    Awww that makes me feel better! Thank you!


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    (Original post by anoymous1111)
    Awww that makes me feel better! Thank you!


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    You're welcome!
    Feel free to post whenever you have a question!
 
 
 
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