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Topic: Algebra 2/Trig Regents
Replies: 55   Last Post: Jul 1, 2011 6:01 PM

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Nick B

Posts: 3
Registered: 6/21/11
Re: Algebra 2/Trig Regents
Posted: Jun 22, 2011 8:46 PM
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I have a few precalc books lying around in my office...here are some of the offerings:

Precalculus by Barnett, Ziegler, Byleen 6th Ed

Definition of an inverse function:

If f is a one-to-one function, then the inverse of f, denoted f^-1, is the function formed by reversing all the ordered points in f. Thus,

f^-1 = {(y, x) | (x, y) is in f}

If f is not one-to-one, then f does not have an inverse and f^-1 does not exist.

Blitzer "Precalculus Essentials" 2nd Edition (I used this book when I taught Precalculus at Stony Brook University a few years ago):

Definition of an Inverse Function:

Let f and g be two functions such that

f(g(x)) = x for every x in the domain of g

and

g(f(x)) = x for every x in the domain of f

The function g is the inverse of the function of f and is denoted by f^-1 (read "f-inverse"). Thus f(f^-1(x)) = x and f^-1(f(x)) = x. The domain of f is equal to the range of f^-1 and vice versa.

Precalculus: Graphs and Models 3rd Ed by Bittinger, Beecher, Ellenbogen, and Penna Page 350

If the inverse of f is also a function, it is named f^-1 (read "f-inverse")

Functions Modeling Change by Connally, Hughes-Hallett, Gleason etc. (these are the same authors of the Reform Calculus books):

Definiton of an Inverse Function:

Suppose Q = f(t) is a function with the property that each value Q determines exactly one value of t. Then f has an inverse function, f^-1 and

f^-1(Q) = t if and only if Q = f(t)

If a function has an inverse, it is said to be invertible

This book goes on to talk about y = sin^-1(x) and y = cos^-1(x) as inverse functions.

I think you could probably find a few books that allow f^-1(x) to be a relation and not a function, but I think the vast majority would not take this approach. Then again, it's not a battle of how many textbooks one can find to back up his or her conventions. It seems as though there are two ways to approach the notation f^-1, so I think SED got it right in the end.


Date Subject Author
6/20/11
Read Algebra 2/Trig Regents
Jayson Kiang
6/20/11
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rhoffman@wacs2.wnyric.org
6/21/11
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Lin Chen
6/21/11
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precopio@nycap.rr.com
6/21/11
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Kathy
6/22/11
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Glenn Mary
6/23/11
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6/23/11
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6/23/11
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Jason
6/22/11
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SRothwell@e1b.org
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John
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StGOLD2112@aol.com
6/22/11
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Nick B
6/23/11
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precopio@nycap.rr.com
6/23/11
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6/23/11
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MHulton@holland.wnyric.org
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6/24/11
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