We cover the idea of function composition and it’s effects on domains and ranges.

 Let’s give an example in a “real context.”

Composition of functions can be thought of as putting one function inside another. We use the notation

Now let’s try an example with a more restricted domain.

Compare and contrast the previous two examples. We used the same functions for each example, but composed them in different ways. The resulting compositions are not only different, they have different domains!

Here is a video on this!

1 : Function composition could be described as...
A huge pain that I wish didn’t exist. The process of stringing relations together, one after the other. A process to combine functions arbitrarily. A purely mathematical process without any real contextual analog. A necessary evil.