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Thread: f(f(x)) problem

  1. #1
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    f(f(x)) problem

    Can someone give me advice on this brain scrambler?

    6x-8 is the output, but I must find f(x) in order to input f(f(x)) to create such an output.
    Any ideas on how to tackle this problem?
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  2. #2
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    Re: f(f(x)) problem

    Quote Originally Posted by bossbasslol View Post
    Can someone give me advice on this brain scrambler?

    6x-8 is the output, but I must find f(x) in order to input f(f(x)) to create such an output.
    Any ideas on how to tackle this problem?
    I think this might be your interpretation of the problem. Can you state the problem exactly as it was stated to you?
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  3. #3
    MHF Contributor MarkFL's Avatar
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    Re: f(f(x)) problem

    I would assume $\displaystyle f(x)$ is linear:

    $\displaystyle f(x)=ax+b$

    And then:

    $\displaystyle f(f(x))=a(ax+b))+b=a^2x+(a+1)b=6x-8$

    Equating coefficients, we then have:

    $\displaystyle a^2=6$

    $\displaystyle (a+1)b=-8$

    Can you proceed?
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  4. #4
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    Re: f(f(x)) problem

    You have helped me a ton lately, and yes, this is the concept I was looking for. As long as I have the grasp of a and b, I can solve for them and continue on. Thank you for your kick starter.
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