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Everyday Applications of Inverse Functions

Date: 11/06/2011 at 07:36:33
From: Eloisa
Subject: Practical applications of inverse functions

I will be reporting about inverse functions and their practical
applications, sort of like what you've answered before: 

But I was wondering if you could help me further. I need some literal
applications, like how exponential growth is used for computing population
and simple interest. I need an actual or concrete example of their use(s)
in today's world.

Thank you! :)

Date: 11/07/2011 at 23:17:35
From: Doctor Peterson
Subject: Re: Practical applications of inverse functions

Hi, Eloisa.

Essentially, an inverse function is the same as solving an equation (when
there is only one solution). When you find the inverse function, you are
simply solving for what was the independent value, in terms of what was
the dependent value.

Any time you need to solve the same kind of equation over and over again,
a more efficient way to do it is to find the inverse (solving once), and
then just apply the inverse (as a formula) each time. For example, if you
had a function that told you how much a quantity x of something cost, and
you wanted to know how many you could make for any given cost, you could
find the inverse function and apply that to any cost you get.

Or, as someone recently discussed with us, if you had a function that told
how high (h) a bathtub fills in any given time t, the inverse function
(which you'd probably just work out as a table) would tell you how long
(t) you can leave the room if you want to fill it to a given height h.

Some functions are used precisely because they are inverses. You use the
logarithm function to solve exponential equations (as in your examples)
because it undoes exponentiation. You use the inverse sine to solve
equations involving the sine. And so on.

You can make that more concrete by picking a particular application, but
you can see that inverses pop up everywhere.

- Doctor Peterson, The Math Forum 
Associated Topics:
High School Functions

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