Function Composition

In this lesson, we will learn how to compose functions, decompose functions, and find the domain of a composite function. When we have a composite function, it's essentially just us taking one function and plugging it in as the input for another. Suppose we had f(x) and g(x), the f(g(x)) or (f o g)(x) is just found by plugging g(x) in for x in f(x). A somewhat harder task occurs when we need to find the domain of a composite function. For this, we need to think about the intersection of the domains of the input function and the newly formed composite function. Lastly, when we decompose a function, we are breaking it up into two simpler functions.