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Thread: Find Function g

  1. #1
    Senior Member harpazo's Avatar
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    Find Function g

    Given f(x) = 3x + 1 and (f + g)(x) = 6 - (x/2), find the function g.

    I know that (f + g)(x) = f(x) + g(x).

    My Set up:

    f(x) + f(x) + g(x)

    3x + 1 + 6 - (x/2)

    I must then simplify.

    Correct thus far?
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  2. #2
    MHF Contributor
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    Re: Find Function g

    Quote Originally Posted by harpazo View Post
    Given f(x) = 3x + 1 and (f + g)(x) = 6 - (x/2), find the function g.

    Correct thus far?
    no. In fact I have no idea what you are doing.

    $g(x) = (f+g)(x) - f(x)$

    $g(x) = \left(6-\dfrac x 2\right) - (3x+1)$

    now simplify
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  3. #3
    Senior Member harpazo's Avatar
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    Re: Find Function g

    Quote Originally Posted by romsek View Post
    no. In fact I have no idea what you are doing.

    $g(x) = (f+g)(x) - f(x)$

    $g(x) = \left(6-\dfrac x 2\right) - (3x+1)$

    now simplify
    I never saw a problem like this before. Thanks. I will work on it.
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  4. #4
    Senior Member harpazo's Avatar
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    Re: Find Function g

    g(x) = 6 - x/2 - (3x + 1)

    g(x) = (12 - x)/2 - (3x + 1)/1

    g(x) = (12 - x -2(3x + 1)/2

    g(x) = (12 - x - 6x - 2)/2

    g(x) = (10 - 7x)/2

    g(x) = 5 - (7x/2)

    Correct?
    Last edited by harpazo; Dec 2nd 2018 at 08:46 PM.
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  5. #5
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    Re: Find Function g

    Quote Originally Posted by harpazo View Post
    g(x) = 6 - x/2 - (3x + 1)

    g(x) = (12 - x)/2 - (3x + 1)/1

    g(x) = (12 - x -2(3x + 1)/2

    g(x) = (12 - x - 6x - 2)/2

    g(x) = (10 - 7x)/2

    g(x) = 5 - (7x/2)

    Correct?
    using this function does $(f+g)(x) = 6 - \dfrac x 2$ ?

    You need to learn to be able to check your own work, and I don't want to hear about your limited time.
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  6. #6
    Senior Member harpazo's Avatar
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    Re: Find Function g

    f(x) + g(x)

    3x + 1 + 5 - (7x/2)

    6 + 3x - (7x/2)

    6 + (3x/1) - (7x/2)

    6 + (6x - 7x)/2

    6 - (x/2)

    It proves to be correct.

    So, g(x) = 5 - (7x/2) is the correct answer.
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