Function Differences: f and f(n) vs. (f \circ g)(n)

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

The discussion clarifies the distinction between a function and its value at a specific point, specifically addressing the notation f versus f(n). It establishes that f represents the function itself, while f(n) denotes the output of the function at the input n. The composition operator (f \circ g) acts on functions rather than their values, making the expression f(n) \circ g(n) incorrect. Instead, the correct formulation is f(g(n)), which maintains the integrity of function composition.

PREREQUISITES
  • Understanding of basic function notation in mathematics
  • Familiarity with function composition
  • Knowledge of mathematical operators such as \circ
  • Basic algebraic manipulation skills
NEXT STEPS
  • Study the properties of function composition in detail
  • Learn about different types of functions and their notations
  • Explore the implications of function values versus function definitions
  • Investigate common errors in mathematical notation and how to avoid them
USEFUL FOR

Students of mathematics, educators teaching function concepts, and anyone looking to deepen their understanding of function notation and composition.

Swapnil
Messages
459
Reaction score
6
What is exactly the difference between f and f(n) and why can't we write (f \circ g)(n) as f(n) \circ g(n)?
 
Last edited:
Mathematics news on Phys.org
f is the function, f(n) is the value of the function at the point n. The ball operator \circ acts on functions, not values, so your second expression is wrong.
 
You can, however, write it as f(g(n)).
 
u can write it
no proplem...i thenk
 
Last edited by a moderator:

Similar threads

Undergrad Can the same argument be used for both radians and degrees in the sine function?
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Best way to fit three functions
  • · Replies 2 ·
Replies
2
Views
1K
MHB Compute $\sum_{n=1}^{2020} (f(n)-g(n))$
  • · Replies 1 ·
Replies
1
Views
1K
Undergrad On inverse function theorem in Spivak's CoM
  • · Replies 6 ·
Replies
6
Views
3K
High School Why do we call function a Rule
  • · Replies 7 ·
Replies
7
Views
1K
Undergrad Doubt about theorem in Calculus on Manifolds
  • · Replies 9 ·
Replies
9
Views
3K
MHB Find all functions satisfying f(mn)=f(m)f(n), and m+n|f(m)+f(n)
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad Why is it important to convert angle units when using trigonometric functions?
  • · Replies 8 ·
Replies
8
Views
2K
Undergrad The Road to Reality - exercise on scalar product
  • · Replies 36 ·
2
Replies
36
Views
5K
Undergrad Significance of discovering a function which computes the n-th prime?
  • · Replies 10 ·
Replies
10
Views
2K