Nick B
Posts:
3
Registered:
6/21/11


Re: Algebra 2/Trig Regents
Posted:
Jun 22, 2011 8:46 PM


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 onetoone 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 onetoone, 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 "finverse"). 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 "finverse")
Functions Modeling Change by Connally, HughesHallett, 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.

