Composite Functions A composite function is a function that is formed by applying a function to the output of another function. In simpler terms, it's like b...
A composite function is a function that is formed by applying a function to the output of another function. In simpler terms, it's like baking a cake and then decorating it with candy.
Let's say we have two functions:
f(x) = x + 2
g(x) = x – 3
The composite function f(g(x)) would be:
This shows that the output of f(g(x)) is equal to the input x – 1.
Here are some more examples of composite functions:
f(x) = x^2
g(x) = x + 1
f(x) = (x + 1)/2
These functions can be combined in a variety of ways to create new functions. For example:
(f(x))² = f(x)^2
(g(x))² = g(x)^2
These composite functions can be used to model real-world situations. For example, we can use a composite function to model the distance a ball travels when it is launched into the air