Calculating a Bijective Function: f(N0)

  • Context: Undergrad 
  • Thread starter Thread starter blob84
  • Start date Start date
  • Tags Tags
    Function
Click For Summary
SUMMARY

The function f: x ∈ Q → (5x-7)/6 is established as bijective. The calculated values for f(N0) include f(0) = -7/6, f(1) = -1/3, f(2) = 1/2, and f(3) = 4/3. To generalize the set that includes the image of f(N0), it is confirmed that the denominator remains constant at 6, while the numerator can take on values defined by the expression 5N - 7 for N in the natural numbers.

PREREQUISITES
  • Understanding of bijective functions
  • Familiarity with rational functions
  • Basic knowledge of number theory
  • Ability to manipulate algebraic expressions
NEXT STEPS
  • Explore the properties of bijective functions in detail
  • Study rational function transformations
  • Learn about the implications of function images and pre-images
  • Investigate the general form of linear functions and their graphs
USEFUL FOR

Mathematicians, educators, and students interested in advanced algebra, particularly those focusing on functions and their properties.

blob84
Messages
25
Reaction score
0
Hi, i have this function [itex]f : x \in Q \rightarrow (5x-7)/6[/itex]
the function is bijective now i need to calculate:
[itex]f(N0)[/itex]
i get :
[itex]f(0)=-7/6[/itex], [itex]f(1)=-1/3[/itex], [itex]f(2)=1/2[/itex], [itex]f(3)=4/3[/itex], etc...
I need to generalize the set that include the image of [itex]f(N0)[/itex],
but i don't know what could be.
 
Physics news on Phys.org
Let's not simplify the fraction. Then the denominator will always be 6. What can the numerator be?
 

Similar threads

Undergrad What Are the Axioms of Fuzzy Logic and How Do They Extend Boolean Algebra?
  • · Replies 7 ·
Replies
7
Views
3K
Undergrad Is √9x a Bijection from N to R?
  • · Replies 7 ·
Replies
7
Views
2K
'Residence' time distribution function for a Pulse input
  • · Replies 14 ·
Replies
14
Views
5K
Undergrad Calculating the inverse of a function involving the error function
  • · Replies 3 ·
Replies
3
Views
2K
High School Is this a finite argument of the countable infiniteness of the rationals?
  • · Replies 21 ·
Replies
21
Views
4K
Graduate Normalization of Morse potential wavefunctions
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad Cantor's decimal proof that (0,1) is uncountable
  • · Replies 9 ·
Replies
9
Views
6K
MHB Proving Set Equivalence with Set Differences?
  • · Replies 9 ·
Replies
9
Views
2K
Graduate What is the derivation of the exact Maxwell-Boltzmann distribution?
  • · Replies 1 ·
Replies
1
Views
2K
MHB Chain Rule in Difference Calculus
  • · Replies 5 ·
Replies
5
Views
2K