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Give an example of a function f: R → R such that f(x1+x2) ≤ ½ ƒ (x1) + ½{ƒ (x2) for all x1, x2 € R, but f is not convex.

Give an example of a function f: R → R such that f(x1+x2) ≤ ½ ƒ (x1) + ½{ƒ (x2) for all x1, x2 € R, but f is not convex.

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.4: Spanning Sets And Linear Independence
Problem 76E: Let f1(x)=3x and f2(x)=|x|. Graph both functions on the interval 2x2. Show that these functions are...
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Give an example of a function f : R → R such that f(x1+x2) ≤ ½ ƒ (x1) + ½ ƒ (x₂) for all x₁, x2 € R, but f is not convex. this is a very very weird function. The fact that R is a vector space over Q is relevant to its construction.).
Transcribed Image Text:Give an example of a function f : R → R such that f(x1+x2) ≤ ½ ƒ (x1) + ½ ƒ (x₂) for all x₁, x2 € R, but f is not convex. this is a very very weird function. The fact that R is a vector space over Q is relevant to its construction.).
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