this is my problem

Suppose that X ⊆R^n is a convex set and f:X →R is a concave function, prove that the set

{ z∈X | f(z) ≥ f(x) for all x∈X}

is convex.

Can someone help me? I'm clueless on this one...

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- Oct 16th 2010, 05:07 AMkpax1041Question about Convex sets
this is my problem

Suppose that X ⊆R^n is a convex set and f:X →R is a concave function, prove that the set

{ z∈X | f(z) ≥ f(x) for all x∈X}

is convex.

Can someone help me? I'm clueless on this one... - Oct 16th 2010, 05:54 AMCSM
Start by putting in your definitions... Write down what you want to prove, and what you already know.

BTW: here is a solution

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