# Composition of functions (in set)

• 385sk117
In summary, the conversation discusses finding the value of (f o g)(1) for the given functions f and g, where f = {(0,1),(1,2),(2,0),(3,3)} and g = {(0,2),(1,3),(2,0),(3,1)}. Through the discussion, it is determined that the answer is 3 and this is achieved by taking the value of g(1), which is 3, and using it as the input for f, which has a point (3,3) that corresponds to the output of 3.
385sk117

## Homework Statement

A = {0, 1, 2, 3} f and g are functions mapping A to A where
f = {(0,1),(1,2),(2,0),(3,3)} and g = {(0,2),(1,3),(2,0),(3,1)}
find

(f o g)(1)

## The Attempt at a Solution

The answer is 3 but i can not get it..
the (1) on the right side means find the y value whem x = 1
I think my (f o g) thing is not correct but i don't know how to do this..
book just gave me an example but that is totally different from this one.

You know that $(f \circ g)(x)=f(g(x))$?. Can you tell us what value g(1) has?

Last edited:
g(1) would be 3 as g has point (1,3)

Ohh i got it.
g(1) is 3 and as f has point (3,3) the answer is 3
thanks!

Yep that is correct. Now what is the value of f(3)?

Edit: Seems you beat me to it! Yes that's all correct.

## Question 1: What is a composition of functions?

A composition of functions is a mathematical operation where the output of one function is used as the input for another function. It is denoted by f o g and read as "f composed with g".

## Question 2: How do you perform a composition of functions?

To perform a composition of functions, you first evaluate the inner function using the input value. Then, take the output of the inner function and use it as the input for the outer function. Finally, evaluate the outer function to get the final output.

## Question 3: What is the domain and range of a composition of functions?

The domain of a composition of functions is the set of all input values for which both functions are defined. The range is the set of all resulting output values after performing the composition.

## Question 4: Is the composition of functions commutative?

No, the composition of functions is not commutative. This means that the order in which the functions are composed matters. In other words, f o g may not be equal to g o f.

## Question 5: How can composition of functions be applied in real-world scenarios?

Composition of functions is a powerful tool used in various fields such as economics, physics, and computer science. It can be used to model real-world processes and phenomena, analyze data, and make predictions. For example, in economics, the demand function can be composed with the supply function to determine the equilibrium price and quantity for a product.

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