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".
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.
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.
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.
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.