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Math Help - Simple Question about showing convex:

  1. #1
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    Simple Question about showing convex:

    Show that the following function, having domain {0.1. ...., n -1 }, is convex:

    f(j) = 1/ (n-j).


    I don't understand how to deal with the domain part and what it means, I am very new to discrete math...please help me and explain...Thank you
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  2. #2
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    Quote Originally Posted by sunnysky777 View Post
    Show that the following function, having domain {0.1. ...., n -1 }, is convex:

    f(j) = 1/ (n-j).
    How does the textbook define convex functions?
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  3. #3
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    Definition:

    Let f be a function whose domain is the set of integers, and define the function g by

    g (i) = f(i) - f(i-1))
    we say that f is a convex function if g is an increaseing fuction; that is, f is convex if for all i,

    f(i+1) - f (i) > or = f(i) -f (i-1).

    Thank you
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  4. #4
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    Quote Originally Posted by sunnysky777 View Post
    Definition:
    Let f be a function whose domain is the set of integers, and define the function g by
    g (i) = f(i) - f(i-1))
    we say that f is a convex function if g is an increaseing fuction; that is, f is convex if for all i,
    f(i+1) - f (i) > or = f(i) -f (i-1).
    Well then apply that definition to the function f(j)=\frac{1}{n-j} where j\in \{0,1,...,n-1\}.
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