What does the small circle symbol in (f◦g)(x) mean

In summary, the "◦" symbol in (f◦g)(x) represents the composition of two functions, with g being evaluated first and its output used as the input for f. This is different from f(g(x)) where g is evaluated first and its output is used directly as the input for f. (f◦g)(x) can be simplified as f(g(x)), but it may be useful to keep the composition form for understanding. To evaluate (f◦g)(x), evaluate g(x) first and then use the output as the input for f. There are limitations when using this notation, such as compatibility of domains and order of operations.
  • #1
pawball
1
0
have not seen this anywhere I've looked, anyone know?
 
Mathematics news on Phys.org
  • #2
It's function composition notation. Same thing as f(g(x))
 
  • #3

The small circle symbol in (f◦g)(x) represents the composition of two functions, f and g. It means that the output of g is being used as the input for f. In other words, the result of g(x) is being plugged into f(x). This notation is commonly used in mathematics to show a sequence of operations on a variable. I hope this helps.
 

1. What does the "◦" symbol mean in (f◦g)(x)?

The "◦" symbol in (f◦g)(x) represents the composition of two functions. It is read as "f composed with g" and indicates that the output of g is used as the input for f.

2. How is (f◦g)(x) different from f(g(x))?

While both (f◦g)(x) and f(g(x)) represent the composition of two functions, their order of operations is different. (f◦g)(x) indicates that g is evaluated first and then the output is used as the input for f. In f(g(x)), g is evaluated first and then the output is used directly as the input for f.

3. Can (f◦g)(x) be simplified or rewritten in any way?

Yes, (f◦g)(x) can be rewritten as f(g(x)). However, in some cases, it may be more useful to keep the composition form for easier understanding and visualization of the functions involved.

4. How do I evaluate (f◦g)(x)?

To evaluate (f◦g)(x), first evaluate g(x) and then use the output as the input for f. This can be done by substituting g(x) into the expression for f(x) and simplifying the resulting expression.

5. Are there any restrictions or limitations when using the composition notation (f◦g)(x)?

One limitation of using the composition notation is that the domains of f and g must be compatible. This means that the output of g must be a valid input for f. Additionally, the order of operations matters when evaluating (f◦g)(x), so it is important to pay attention to the order in which the functions are composed.

Similar threads

Replies
12
Views
917
  • General Math
Replies
3
Views
831
Replies
2
Views
1K
  • General Math
Replies
8
Views
1K
Replies
10
Views
1K
  • Quantum Physics
Replies
1
Views
686
  • Quantum Physics
Replies
5
Views
746
Replies
7
Views
2K
  • General Math
Replies
7
Views
1K
Back
Top