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Composite function help please. :) Watch

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    Hello there,

    Cold someone tell me how I would work out fg where f(x) = 3e^2x and g(x)=ln4x. I know how to form a composite function i'm just stuck on what to do as there is and e and ln in the equation. Thanks!
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    The same way as you usually would. What do you get when you do it? Post your working. Also, is that exp(2x) or exp^2(x)?
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    (Original post by little_wizard123)
    The same way as you usually would. What do you get when you do it? Post your working. Also, is that exp(2x) or exp^2(x)?
    Hi, it's exp^2x, sorry.

    My working is:-

    (3)(e^(2)(ln4x)) = fg. Is this correct? Is this all I can do? Thanks!
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    You can use a log rule to simplify it. And then use the fact that ln(x) and e^x are inverses of each other.
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    (Original post by apo1324)
    Hi, it's exp^2x, sorry.

    My working is:-

    (3)(e^(2)(ln4x)) = fg. Is this correct? Is this all I can do? Thanks!
    If you mean  3e^{2\ln{(4x)}} , then that's right.

    You can simplify it more though. Note that  e^{\ln{(\mbox{stuff})}} = \mbox{stuff}
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    (Original post by Daniel Freedman)
    If you mean  3e^{2\ln{(4x)}} , then that's right.

    You can simplify it more though. Note that  e^{\ln{(\mbox{stuff})}} = \mbox{stuff}
    Is the answer just 12x? Thanks. Also, if the domain of f was (-infinite,infinite), and the domain of g was (0,infinite):-

    Would the domain of fg be [0,infinite) and the range of fg be [0,infinite)?? I don't know if this is correct.
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    (Original post by apo1324)
    Is the answer just 12x? Thanks. Also, if the domain of f was (-infinite,infinite), and the domain of g was (0,infinite):-

    Would the domain of fg be [0,infinite) and the range of fg be [0,infinite)?? I don't know if this is correct.
    Nope. You can't use exp (ln(x)) = x if there is a number in front of the log. You need to use the rule that a*ln(x) = ln(x^a) first.
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    (Original post by little_wizard123)
    Nope. You can't use exp (ln(x)) = x if there is a number in front of the log. You need to use the rule that a*ln(x) = ln(x^a) first.
    Is it this:-

    3e^ln4x^2?
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    (Original post by apo1324)
    Is it this:-

    3e^ln4x^2?
    (4x)^2 which is 16x^2.
 
 
 
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