Date: 01/25/2002 at 10:08:33
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
Thanks so much.
Here is the response:
Date: 01/25/2002 at 23:22:52
From: Doctor Peterson
Subject: Re: Inverse functions
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
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.