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Inverse Functions in Real Life


Date: 01/25/2002 at 10:08:33
From: Denise
Subject: Inverse functions

I would like to know if you have a good example of how inverse 
functions would be used in real life. I am teaching my students this 
concept and the book I am using does not really include any 
applications.

Thanks so much.


Date: 01/25/2002 at 23:22:52
From: Doctor Peterson
Subject: Re: Inverse functions

Hi, Denise.

Let's see ...

If they've ever used a square root, they've used an inverse function!

Whenever they undo something that they or someone else did, they use 
an inverse function, whether it's untying a knot or solving a puzzle 
or decoding a secret message. When a computer reads a number you type 
in and converts it to binary for internal storage, then prints it out 
again on the screen for you to see, it's doing an inverse function.

If they know even a little trigonometry, they should know about the 
arctan function, the inverse of the tangent. And if they have used 
logarithms, they should know that a logarithm is the inverse of an 
exponential. These are used constantly in real life. (At least in the 
real life of people who use these sorts of math in their work, which 
is more than students realize.)

How do you define "real life"? 

Does it have to be part of a kid's everyday experience outside of 
school, as opposed to something engineers do every day to design the 
devices kids use every day? I think "real life" is a lot bigger than 
most students realize! And most interesting applications of math occur 
in the context of other math, science, or engineering, rather than in 
the ordinary activities of life, so it's not realistic to pretend 
everyone will be using advanced math whenever they go shopping or 
something, or that anything outside their experience is unimportant. 
(This is what I wish I could say to all the students who write to us 
asking how topic X is used in real life, or to the teachers who 
apparently assign them to find out.)

I'll assume you are not trying to show the importance of inverse 
functions, but just looking for a way to relate the concept to 
something familiar.

How about this: When someone calls you on the phone, he or she looks 
up your number in a phone book (a function from names to phone 
numbers). When Caller ID shows who is calling, it has performed the 
inverse function, finding the name corresponding to the number.

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/   
    
Associated Topics:
High School Functions

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