Our goal in Calculus is to analyze functions.
This means describing the function’s behavior.
Calculus will provide procedures for obtaining the derivative of any function. However, for compositions, we can get the same behavior information right now.
Let \(f\) be a function with domain \(D_f\).
Let \(g\) be a function with domain \(D_g\).
Then the composition of f and g, \(f \circ g\), is defined as
The value of \(g\) becomes a domain number for \(f\).
The composition is defined on a subset of the domain of \(g\). The composition is defined at those numbers in the domain of \(g\) where the value of \(g\) is in the domain of \(f\).
Learning Outcomes
In this section, students will
- view functions as compositions.
- deduce behavior of compositions.
ooooo-=-=-=-ooOoo-=-=-=-ooooo
more examples can be found by following this link
More Examples of Composition