Is the Function f(x) = 2x + 3 Continuous Over All Real Numbers?

  • Context: Undergrad 
  • Thread starter Thread starter evagelos
  • Start date Start date
  • Tags Tags
    Continuity Proof
Click For Summary
SUMMARY

The function f(x) = 2x + 3 is continuous over all real numbers, R. This conclusion is based on the definition of continuity, which states that a function is continuous at a point if the limit of the function as it approaches that point equals the function's value at that point. Since f(x) is a polynomial function, it is continuous everywhere on its domain, which is all real numbers.

PREREQUISITES
  • Understanding of the definition of continuity in mathematics
  • Familiarity with polynomial functions and their properties
  • Basic knowledge of limits and their application
  • Ability to construct formal mathematical proofs
NEXT STEPS
  • Study the formal definition of continuity in calculus
  • Learn about the properties of polynomial functions
  • Explore the concept of limits and their role in continuity
  • Practice constructing formal proofs in mathematical analysis
USEFUL FOR

Students of calculus, mathematics educators, and anyone interested in understanding the continuity of functions and formal proof techniques.

evagelos
Messages
314
Reaction score
0
Give a formal proof that the function , f(x) = 2x + 3 is continuous over the real Nos R
 
Physics news on Phys.org
Why?
 
What is the definition of "continuous on a set"? That is a good place to start.

Hurkyl is saying "It's your question- you go first!"
 

Similar threads

Undergrad What Are the Axioms of Fuzzy Logic and How Do They Extend Boolean Algebra?
  • · Replies 7 ·
Replies
7
Views
3K
Undergrad Contrapositive of theorem and issue with proof
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad Max of 3 random cards from deck vs max of 3 numbers from 1-13
  • · Replies 5 ·
Replies
5
Views
2K
Can this function still be a constant function?
  • · Replies 11 ·
Replies
11
Views
2K
Undergrad On pdf of a sum of two r.v.s and differentiating under the integral
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Calculating the inverse of a function involving the error function
  • · Replies 3 ·
Replies
3
Views
2K
Assume that if the real-valued function h(x) is Lipschitz continuous...
  • · Replies 22 ·
Replies
22
Views
2K
Show that the given function is continuous
  • · Replies 27 ·
Replies
27
Views
2K
f(x) = 2x+1, proving that it is continuous when p = 1 with 𝛿 and ε
  • · Replies 7 ·
Replies
7
Views
2K
Undergrad Is √9x a Bijection from N to R?
  • · Replies 7 ·
Replies
7
Views
2K