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Math Help - Set Theory-Finding the Relative Complement of Two Functions

  1. #1
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    Set Theory-Finding the Relative Complement of Two Functions

    My question is this:
    How do you find the relative complement between two functions?

    f(x)=x+2 {3,4,5,6,7...}
    f1(x)=3x {3,6,9,12...}

    {x+2\3x}

    Should give you the sequence: {4,5,7,8...}

    Is it possible to find a new function that will predict this sequence?
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  2. #2
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    Quote Originally Posted by joeday View Post
    My question is this:
    How do you find the relative complement between two functions?

    f(x)=x+2 {3,4,5,6,7...}
    f1(x)=3x {3,6,9,12...}

    {x+2\3x}

    Should give you the sequence: {4,5,7,8...}

    Is it possible to find a new function that will predict this sequence?
    the answer is: g(x)=3\left[\frac{x+2}{2}\right] + (-1)^{x+1}, \ \ x = 1,2,3, \ ... , where [a] is the integer part of a.

    that was quite easy to find if you note that the elements of the sequence are in the form 3k \pm 1.
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  3. #3
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    Thankyou

    Thankyou for your help,

    Is it possible to find an answer using just the functions, without knowing what the sequence will be??
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