Logo
Home Study Material Contact Search
AI Chat FREE
  1. mathematics
  2. advance math
  3. a) let s ? r, assuming that f : s ? r is a continu

a) Let S ? R, assuming that f : S ? R is a continuous...

90.2K

Verified Solution

Question

Advance Math

a) Let S ? R, assuming that f : S ? R is a continuous function,if the
image set {f(x); x ? S} is unbounded prove that S is unbounded.


b) Let f : [0, 100] ? R be a continuous function such that f(0) =f(2),
f(98) = f(100) and the function g(x) := f(x+ 1)?f(x) is equal tozero in at most
two points of the interval [0, 100].

Prove that (f(50) ? f(49))(f(25) ? f(24)) > 0.

Answer & Explanation Solved by verified expert
4.3 Ratings (898 Votes)
    See Answer
Get Answers to Unlimited Questions

Join us to gain access to millions of questions and expert answers. Enjoy exclusive benefits tailored just for you!

Membership Benefits:
  • Unlimited Question Access with detailed Answers
  • Zin AI - 3 Million Words
  • 10 Dall-E 3 Images
  • 20 Plot Generations
  • Conversation with Dialogue Memory
  • No Ads, Ever!
  • Access to Our Best AI Platform: Flex AI - Your personal assistant for all your inquiries!
Become a Member

Other questions asked by students

Physics
1.2K views

We've landed on the moon, Mars and Venus. Mankind has spent months even years in space. Pick...

Physics
1.2K views

Patch-Clamp instruments allow researchers to measure the opening and closing of a single channel in a...

Physics
1.2K views

A stone is dropped into a river from a bridge 43.0 m above the water. Another...

General Management
1.2K views

This article is from 1999 and the contents pretty much hold true today. Considering what is...

Biology
1.2K views

De etoliation is a plant s way of responding to A loss of water B...

Basic Math
1.2K views

Marina has learned that it typically rains 43% of the days in August in the...

Statistics
1.2K views

study was conducted to determine how people get jobs The table below lists ata from...

Calculus
1.2K views

In Silicon Valley a number of computer firms were found to be contaminating underground water...

Algebra
1.2K views

2 Use the following data obtained from ages of the last six U S Presidents...

Accounting
1.2K views

Round the answers to nearest cent. Instructions: 1. Determine for each plan the earnings per...

Accounting
1.2K views

Puget Sound Divers provides diving services, such as underwater ship repairs, to its clients. The...

Accounting
1.2K views

What are the forecasting models used in qualitative techniques? Elaborate on each one of them...