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Math Help - Problem on basic functions clarification

  1. #1
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    Problem on basic functions clarification

    Given x2g(x) + g(1-x) = 2x-x4, the problem is to find g(0). What I did was I evaluated the equation using 0. It therefore becomes:
    (0)g(0) + g(1-0) = 0
    g(1) = 0

    Then, I evaluated the equation with 1 so it becomes:

    1g(1) + g(1-1) = 2-1
    g(1) + g(0) = 1
    Since g(1) = 0, then:
    g(0) = 1.

    I'm not really sure if what I did was right, because the solution seems too simple. I would like to ask for clarification if what I did was right.

    Thanks in advance.
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  2. #2
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    Re: Problem on basic functions clarification

    Looks good to me.

    If it seems too easy why not try to find out more about the function?
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  3. #3
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    Re: Problem on basic functions clarification

    If you see the points of g(x) you can easily derive the functions so it has the points (0,1)..(1,0)

    This can be interpreted as a parabola

    g(x)=-x^2+1 \Rightarrow g(0)=1 \,\,\, g(1)=0

    Now If your calculation is correct that should satisfy the equation you gave

    x^2g(x)+g(1-x)=2x-x^4

    x^2(1-x^2)+(1-(1-x)^2)=2x-x^4

    x^2-x^4+1-x^2+2x-1=2x-x^4

    0=0 \,\, so your calculation is correct ...
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  4. #4
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    Re: Problem on basic functions clarification

    Thanks for your help. At least I know I'm on the right track.
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