Do you know of a real world example where you'd combine two functions into a composite function? I see this topic in Algebra 2 textbooks, but rarely see actual applications of it. It's usually plug and chug where you take f(g(4) and run it through both functions. This leads to the idea of creating a composite function f(g(x). But it's somewhat academic, and it's not like you're saving time b/c you need to run 50 different numbers through both functions.
While on this topic, where is this topic used in later math? In Precalculus, you can determine the domain of the composite function. In Calc, composition is used to describe the ideas behind the Chain Rule. In Calc, you break down a function into the 2 components to show it's continuous. (If the components are continuous, so is the composite function) Any other main areas?
Thanks!
Best Answer
You use composite functions whenever you buy a sale (discounted) item. When you are standing in the store trying to decide if you can afford the item, the first thing you calculate is the discount. For example, I want to buy this 20 dollar shirt, and it is on sale at 15% off. This means that the shirt is really 17 dollars. Now, you must calculate what the shirt will cost after sales tax (let's say it is 8%). Your total cost for the shirt after the discount and sales tax will be $18.36. This process of computation can be expressed as a composite function.
If f(x) = The price of the shirt after the discount and g(x) = The price after sales tax then,
The function for the final cost of the shirt = g(f(x)).