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Math Help - 2 functions F(x) and G(x)

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    Exclamation 2 functions F(x) and G(x)

    Two functions are defined as





    and

    I have been stuck on this question for a long time and I have to find:





    and



    So can somebody please either give me the results with showing the process or just help me through with a detailed explanation.
    I would be very grateful
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    Re: 2 functions F(x) and G(x)

    Quote Originally Posted by leonm92 View Post
    Two functions are defined as





    and

    I have been stuck on this question for a long time and I have to find:





    and



    So can somebody please either give me the results with showing the process or just help me through with a detailed explanation.
    I would be very grateful
    Evaluate g at x = -4, then put this value as x in f.

    Follow a similar process for the second...


    Edit: I think I may have made a mistake. Are you using fg and gf as the multiplication of the two functions or the composition of the two functions? If it's the latter, follow what I did...
    Last edited by Prove It; August 6th 2012 at 04:11 AM.
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    Re: 2 functions F(x) and G(x)

    I don't know to be honest but I followed what you said and it worked for both. Could you tell me what to do with please
    Last edited by leonm92; August 6th 2012 at 04:32 AM.
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    Re: 2 functions F(x) and G(x)

    Quote Originally Posted by leonm92 View Post
    I don't know to be honest but I followed what you said and it worked for both. Could you tell me what to do with please
    Can you evaluate the inverse function of f? Write it as y = , then swap the x and the y values and transpose.
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    Re: 2 functions F(x) and G(x)

    I've just been reading over it but I can't get my head around it
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    Re: 2 functions F(x) and G(x)

    f(x) = y = \frac{2x+9}{-4x-5}

    swap x and y (because that is what an inverse function does ... )

    x = \frac{2y+9}{-4y-5}

    solve for y ...
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