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Math Help - [SOLVED] find a and b? Simple problem

  1. #1
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    [SOLVED] find a and b? Simple problem

    Hi, I have tried this problem a few times.

    Fx=ax+b

    gx=x^2+x+1

    gfx=x^2-5x+7

    Not sure where I'm going wrong. A few tips would be appreciated.
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  2. #2
    MHF Contributor harish21's Avatar
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    Quote Originally Posted by Neverquit View Post
    Hi, I have tried this problem a few times.

    Fx=ax+b

    gx=x^2+x+1

    gfx=x^2-5x+7

    Not sure where I'm going wrong. A few tips would be appreciated.
    Your notation is unclear. Did you mean this?

    f(x) = ax+b

    g(x) = x^2+x+1

    g(f(x)) = x^2-5x+7

    ??
    Last edited by harish21; April 23rd 2010 at 11:32 PM.
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  3. #3
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    correction

    yes it should be f(x),g(x) and gf(x)
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  4. #4
    MHF Contributor harish21's Avatar
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    Quote Originally Posted by Neverquit View Post
    yes it should be f(x),g(x) and gf(x)
    IF
    f(x) = ax+b

    g(x) = x^2+x+1


    then,

    g(f(x)) = (ax+b)^2+ (ax+b)+1 .......(I)

    expand this..

    Given g(f(x)) = x^2-5x+7.........(II)

    equate (I) and (II) to find a and b.
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  5. #5
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    update

    Hi,
    I did set the equations together in the first place. Now I have had another look and have solved for b.
    Thanks!
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  6. #6
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    Update

    From ax^2+ 2abx+b^2+ax+b+1= x^2-5x+7
    Set x=0
    b^2+b-6=0
    (b+3)(b-2)…b=-3,2

    For 'A' st b=-3, A=1....or...st b=2, A=-1
    Last edited by Neverquit; April 24th 2010 at 04:17 AM. Reason: correction
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