I am currently teaching composition of functions in my Algebra II class. My students are still learning it and have not gotten around to the question of when it is used in real life.
The thing is, I've never been told how to use it in real life. I know I use it to determine if two functions are inverses of each other but I have no idea otherwise.
I read of a beautiful example showing a f(g(x)) that cannot be done in the reverse. You are bottling soda in bottles. You have one function which fills the bottle while the other function puts the cap on.
So where in real life do we see composite functions used? Quite a few places it turns out.
1. Predator - Prey situations where there are outside influences such as a virus or another predator.
2. The population living near the coast effects the number of whales which effects the amount of plankton available.
3. The salary based on a commission for anything sold over a minimum amount.
4. Calculating the cost of life insurance based on age.
5. Buying something, paying tax, and paying a delivery fee is another example of composite functions.
6. A circle whose radius increases over time.
7. A vehicle uses so much gas per hour and there is a cost for the gas. So the two functions combined are the composite functions.
8. The duration of a cruise as a function of the the speed of the river.
So basically anything that is based on something else tends to be a composition of functions and is all around us. So many possible examples.
I love finding out we do use composite functions everywhere in life. Let me know what you think. Have a good day.