My students often ask how do I use this in real life. Its a good question because I've never really thought of where it is used. Its just not something I ever think about.
So to start out, this prezi introduces functions and their inverses by defining them and then focuses on showing how it works through currency conversion. I've always thought of currency conversion as the use of ratios but in the strictest sense it is a function.
For the most part, just about everything I find talks about undoing functions and trig pops up most in regard to inverse functions because you have to use the inverse to find length or the angles. So with that in mind, I discovered that Sophia.org has 5 tutorials on real world examples of inverse trigonometric functions.
Other than that, the most common explanation I find is you are undoing the function. Or as the prezi states, if you convert from the Dollar to the Euro, that is the function and when you convert back from Euro's to the Dollar, you are doing the inverse. Still other than composition of functions to prove two equations are inverses of each other, I'm hard pressed to find solid real life examples.
I've found problems with families buying hot dogs and drinks for $10 and then finding the solution but most people don't calculate inverses per say. I think the other issue is that I focus on the mathematical aspect of inverses rather than inverse being a process of reversing things.
While I was off looking for information on inverse functions, I checked out real world applications of composite functions. I found a slide show with a cool definition that makes total sense and which I plan to use in class. A composite function is nothing more than combining two functions into one to model something. This places composite functions into a framework so I could find lots of examples and use those to introduce this topic.
So the example here is great for showing how to use composite functions to determine which deal is better in the situation. It is something that is quite possible and doesn't sound too artificial. I am off to find more examples. Have a good day.