How would we calculate (f O g)?

  • Thread starter aaa59
  • Start date
In summary, the formula for calculating (f O g) is (f O g)(x) = f(g(x)), where f and g are functions and x is the input value. The domain of (f O g) is determined by the domain of g, while the range is determined by the range of f. (f O g) cannot be calculated without knowing the specific functions f and g. The order of the functions matters in the calculation of (f O g), with g being applied first and its output used as the input for f. An example of calculating (f O g) is f(x) = x^2 and g(x) = 2x+1, resulting in (f O g)(x)
  • #1
aaa59
8
0
if A={1,2,3}

f:A-> A = {(1,2),(2,3),(3,1)}
g:A->A = {(1,2),(2,1),(3,3)}

how would we calculate (f O g)?
 
Physics news on Phys.org
  • #2
say h = f o g. To find h(x), simply plug x into g, and then plug the result into f.

For example, g(2) = 1 and f(1) = 2. So h(2) = 2. Hope this helps.
 
  • #3
i think i got it.

so: g(1) = 2 and f(2) = 3. therefore h(1)=3. am i right?
 
  • #4
Yes.
 
  • #5
At this stage, you can just consider
[tex]h = f \circ g[/tex]
as just "shorthand" for the function defined by
[tex]h(x) = f(g(x))[/tex]
 

1. What is the mathematical formula for calculating (f O g)?

The formula for calculating (f O g) is (f O g)(x) = f(g(x)), where f and g are functions and x is the input value.

2. How do you determine the domain and range of (f O g)?

The domain of (f O g) is determined by the domain of g, as g is the input for f. The range of (f O g) is determined by the range of f, as f(g(x)) will output values within its range.

3. Can (f O g) be calculated if the functions f and g are not given?

No, (f O g) cannot be calculated without knowing the specific functions f and g. The formula for (f O g) requires the functions to be inputted.

4. How does the order of the functions affect the calculation of (f O g)?

The order of the functions matters in the calculation of (f O g). The function g will be applied first to the input value, and then the resulting output will be used as the input for f.

5. Can you provide an example of calculating (f O g)?

Sure, let's say f(x) = x^2 and g(x) = 2x+1. To calculate (f O g), we first plug in g(x) into the input of f(x), which gives us f(g(x)) = (2x+1)^2. Then we can simplify to get (f O g)(x) = 4x^2 + 4x + 1.

Similar threads

  • Linear and Abstract Algebra
Replies
10
Views
2K
  • Linear and Abstract Algebra
Replies
9
Views
1K
Replies
1
Views
1K
  • Programming and Computer Science
Replies
5
Views
859
  • Linear and Abstract Algebra
Replies
8
Views
2K
  • Set Theory, Logic, Probability, Statistics
Replies
20
Views
4K
  • Linear and Abstract Algebra
Replies
7
Views
1K
  • Linear and Abstract Algebra
Replies
16
Views
3K
Replies
24
Views
4K
  • Linear and Abstract Algebra
Replies
6
Views
1K
Back
Top