10.18. For each of the following set-valued functions, draw the graph and determine whether or not F(x) is convex for all values of x in the domain: (a) Let F: R→s R be given by F(x) = {y € R ] y ≤ x}. S (b) Let G: R→s R be given by G(x) = {nx ER In € Z}. (c) Let H: R→s R² be given by H(x) = {(y₁, y2) € R² | y₁ y2 = x}.
10.18. For each of the following set-valued functions, draw the graph and determine whether or not F(x) is convex for all values of x in the domain: (a) Let F: R→s R be given by F(x) = {y € R ] y ≤ x}. S (b) Let G: R→s R be given by G(x) = {nx ER In € Z}. (c) Let H: R→s R² be given by H(x) = {(y₁, y2) € R² | y₁ y2 = x}.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:10.18. For each of the following set-valued functions, draw the graph and determine
whether or not F(x) is convex for all values of x in the domain:
(a) Let F: R→s R be given by F(x) = {y € R | y ≤ x}.
(b) Let G: R→s R be given by G(x) = {nx € R |ne Z}.
(c) Let H: R→s R² be given by H(x) = {(y₁, y2) € R² | y1 y2 = x}.
S
S
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