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Math Help - Convex Set

  1. #1
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    Convex Set

    Show that if f is any convex function and b any real number, then the solution set of the inequality f(x)<=b is a convex set.

    A function is convex if.....

    f(λX(1) + (1 - λ)X(2)) <= λf(X(1)) + (1 - λ)f(X(2))

    where X(1) and X(2) are X subscript 1 and X subscript 2

    I have no clue how to do this. Can someone help me out!!!! TIA!!!
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  2. #2
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    Quote Originally Posted by TreeMoney View Post
    Show that if f is any convex function and b any real number, then the solution set of the inequality f(x)<=b is a convex set.

    A function is convex if.....

    f(λX(1) + (1 - λ)X(2)) <= λf(X(1)) + (1 - λ)f(X(2))

    where X(1) and X(2) are X subscript 1 and X subscript 2

    I have no clue how to do this. Can someone help me out!!!! TIA!!!
    Just note that
    f(λX(1) + (1 - λ)X(2)) <= λf(X(1)) + (1 - λ)f(X(2))<=λ(b)+(1-λ)b=b
    for 0<=λ<=1.
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