This confusion in notation is due to the fact that you are asking for the
inverse of a mathematical object (a function, in this case) without
specifiying the binary operation (multiplication or composition) under which
the inverse is to be taken. And it is simply a special case of the
ambiguity arising from "exponent" notation for functions in general: should
it mean iterated multiplication or iterated composition?
But mathematicians generally prefer to have unambiguous notation, and I have
seen the attempt by at least one author to deal with this problem. He would
reserve $f^3(x)$ or $f^{-1}(x)$ for iterated multiplication or
multiplicative inverse, respectively, of the function, and $f^{\circ 3}$ or
$f^{\circ -1}(x)$ for iterated composition or compositional inverse,
respectively. (To find out how that is really supposed to look, run this
paragraph through some version of TeX.) IMHO, this is an elegant solution.
---------------------------------------------------------------
Kevin Broussard broussard@siskiyous.edu
College of the Siskiyous
800 College Avenue *remember to replace this
Weed, CA 96094 *section with some witty
*quotation or something.
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