Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Let fi : R" –→ R and f2 : R" → R be two functions. (5.1) Consider the following proposition: If epi(fi) N epi(f2) is a convex set, then at least one of the functions fi and f2 is a convex function. Either prove this proposition or give a counterexample (i.e., find two functions fi : R" and f2 : R" → R that satisfy the hypothesis but do not satisfy the conclusion).

Let fi : R" –→ R and f2 : R" → R be two functions. (5.1) Consider the following proposition: If epi(fi) N epi(f2) is a convex set, then at least one of the functions fi and f2 is a convex function. Either prove this proposition or give a counterexample (i.e., find two functions fi : R" and f2 : R" → R that satisfy the hypothesis but do not satisfy the conclusion).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question

can you give me counterexample

Let fi : R" –→ R and f2 : R" → R be two functions. (5.1) Consider the following proposition: If epi(f1) N epi(f2) is a convex set, then at least one of the functions f1 and f2 is a convex function. Either prove this proposition or give a counterexample (i.e., find two functions f1 : R" → R and f2 : R" → R that satisfy the hypothesis but do not satisfy the conclusion).
Transcribed Image Text:Let fi : R" –→ R and f2 : R" → R be two functions. (5.1) Consider the following proposition: If epi(f1) N epi(f2) is a convex set, then at least one of the functions f1 and f2 is a convex function. Either prove this proposition or give a counterexample (i.e., find two functions f1 : R" → R and f2 : R" → R that satisfy the hypothesis but do not satisfy the conclusion).
Expert Solution
steps

Step by step

Solved in 2 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS