Question: please prove this question Let f1 : R > R and f2 : R > R be two functions. (5.1) Consider the following proposition: If

please prove this question

Let f1 : R" > R and f2 : R\" > R be two functions. (5.1) Consider the following proposition: If epi(f1) 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., nd two functions f1 : R\" > R and f2 : R\" > R that satisfy the hypothesis but do not satisfy the conclusion)

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

please give a counterexample Let f1 : R\" > R and f2 : R\" > R be two functions. (5.1) Consider the following proposition: If epi(f1) epi(f2) is a convex set, then at least one of the functions f1...

1. Let f1 : R\" > R and f2 : R\" > R be two functions. (5.1) Consider the following proposition: If epi(f1) epi(f2) is a convex set, then at least one of the functions f1 and f2 is a convex function....

The Basics of Financial Mathematics Spring 2003 Richard F. Bass Department of Mathematics University of Connecticut c These notes are 2003 by Richard Bass. They may be used for personal use or class...

please answer this question thank you Let f1 : R" > R and f2 : R\" > R be two functions. (5.1) Consider the following proposition: If epi(f1) epi(f2) is a convex set, then at least one of the...

1. A player throws a fair die and simultaneously flips a fair coin. If the coin lands heads, then she wins twice, and if tails, then one-half of the value that appears on the die. Determine her...

1. Consider the two points x 1 = (1, 1), x 2 = (1, 0) in R2 . Draw the set of points which can be obtained by using the following operations. (a) x = 1x 1 + 2x 2 , 1, 2 R (linear combination) (b) x =...

3. [NP-Complete Satisflability Problems: 3SAT][30; 5+5+10+10] To solve this problem, you should review the materials from the textbook, Section 10.3.3 "NP-Completeness ofCSAT" and 10.3.4 "NP...

Microkernel operating systems aim to address perceived modularity and reliability issues in traditional "monolithic" operating systems. (i) Describe the typical architecture of a microkernel...

SUMMARY this article for about 2 pages with single spacing. Thank you. ECONOMETRICS: MEASUREMENT I N ECONOMICS1 I As the first incumbent of a new Chair in this University, I thought that in this...

"Fortran, Algol and Lisp invented most programming language concepts 50 years ago; adding the concept of object-orientation suffices to explain all programming languages to date". To what extent is...

Write a program to merge two sorted files into a single file using Linux/UNIX.

For what reasons do auditors obtain an understanding of a clients internal control?

Which inventory method aligns with the natural flow of goods in industries like retail? Specific Identification Method FIFO WACM LIFO

Susan wants to buy a house for $200,000. US Bank will give her the loan at 3.5% for 30 years if she puts 20% down and Dacotah Bank will give her the loan at 3.8% for 30 years if she puts 10% down....

Determine at least one (1) strategy and one (1) process on how these responsibilities must be fulfilled. Briefly describe any additional information you need to communicate information about the work...

(a) Find a power series solution of the nonhomogeneous equation y 4 xy 4 y = e x , about the ordinary point x = 0. (b) Find the singular points of the differential equation ( x 2 9) 2 y + ( x +...

Following data are recorded to investigate the relationship between 3 inputs X 1 , X 2 and X 3 and the output Y X1 X2 X3 Y 3 2 1 4.635801337 3 2 1.5 8.43023389 4 6 2 7.537262868 2 2 3 20.74872142 1 2...

What will happen if variability in beak size is 0? Graph the change in beak size for finches from Darwin and Wallace islands, and indicate which one had 0 variability. *year on x-axis *average beak...

using oy rules of implication QUESTION Construct a proof using only the sight rules of implication. Don't forge 1. (RVN) ( FG) 2. D > 0 3. -C A 4. R.H 5. DVF 7 AVG QUESTION Construct a proof using...

4. It is only at this point that you can give the problem your full attention in relation to the various ways you have framed the problem.

1. To provide an insight into why a communication situation can be perceived differently depending on which psychological framework we choose to use.

4. What is the meaning of this statement, we should always demarcate a problem in accordance with our objectives, or with what we are trying to understand? a) Give at least three examples that shed...