InversesDate: 06/05/2001 at 16:10:28 From: Anonymous Subject: Inverses What is an inverse? Date: 06/05/2001 at 17:07:46 From: Doctor Peterson Subject: Re: Inverses Hi, The word "inverse" is used in many different settings, so you may have to be more specific about what kind of inverse you have in mind. But generally, the word means something that "undoes" something else. For example, the "additive inverse" of a number is the number you can add to it to get zero - in other words, the negative of the number. It is called the inverse because adding it undoes addition of the original number; if I know what x + 3 is, I can add the additive inverse -3 and get the value of x. Similarly, the multiplicative inverse of a number is the number you multiply by to get 1; this is the reciprocal. If I know 3 times x, I can multiply by 1/3, the multiplicative inverse of 3, to find x. We also talk about the inverse of a function. Because x^-1 (x to the negative first power) is the multiplicative inverse, we call the inverse of the function f, f^-1. (This is a little dangerous, but we usually know it doesn't mean the reciprocal of the function.) This is the function that undoes what f does: f^-1(f(x)) = x for all x For example, the inverse of the square f(x) = x^2, for x >= 0 is the square root f^-1(x) = sqrt(x), for x >= 0 because the square root of the square of a (positive) number is the number itself. There are other kinds of inverses, but these are the first you encounter. If you want more details, go to the Dr. Math search page and enter, say, "inverse function". Also, check out the Number Glossary in our FAQ for my first two examples. Or, write back and tell me more about what you need to know. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ |
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