Real Life Inverse Functions.

  I don't know about you but I always teach inverse functions after I teach composite functions.  It has always been easier since you use composite functions to show equations are inverses of each other.

The easiest inverse functions are powers and their equivalent roots such as squared and square roots.  We especially use those two when taking the area of a square room and finding its length by taking the square root.

Another example is when you call someone and their caller id shows your number. What about when you go traveling and you have leftover Peso's?  When you convert it back into American, you are performing an inverse function.  Those currency exchange places you find at airports do the conversions all day long.  Years ago, my sister worked for a company that had dealings with other companies in Canada.  She called me one day to find out how much they needed in Canadian to pay for something so I had to do the calculations. 

On the other hand, if you have convert from metric to standard, you've performed an inverse function because living in the United States, we had to use a formula to convert from standard to metric so when we convert back, we've just performed the inverse function.  Last summer I traveled on a European carrier and their weight limits were all in kilograms so I had to make sure my suitcase did not go over the limits.  I'm going to Germany this summer via a different carrier and I have to deal with kilograms so sometimes we have to use inverse functions regardless of our desires.

Other inverses include things like you know my speed but I need to find how far I traveled to get somewhere so you use the inverse to find how far you went and vice versa.  Its also derivatives and integrals in calculus. On a side note, there is this great book by Elizabeth Moon called Mathamagics.  In it, spells are derivatives and counter spells are antiderivatives.  The heroine keeps messing up when trying to counter spells but her man, a mathematician, is great at casting and countering spells.  Even the chapter numbers are mathematically correct.

One other way to look at inverses is that information is converted in a way that it is not lost in the conversion or it allows us to solve problems much easier.  For instance it is much easier to use ln than e when solving e^x = 50.  Although it is not done as much, people used to use logs to do math when they had certain functions to calculate results from.

Sorry about yesterday but the internet at work went down so I couldn't do anything. Its been down at home most of the time so I haven't even been able to work there.  I went two days with no landline, no cell service, no internet and so I apologize if I miss a day here and there.

Let me know what you think. Have a great day.