Precalc0108to0109-page26

Precalc0108to0109-page26 - (Section 1.9: Inverses of...

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(Section 1.9: Inverses of One-to-One Functions) 1.9.16 2. f n . Many instructors reluctantly use the f ± 1 notation to represent the inverse function of f . • This is because n often represents an exponent in the notation f n , except when n = ± 1. For example, f 2 is often taken to mean ff ; that is, f 2 x () = fx ± ² ³ ´ ± ² ³ ´ . In Chapters 4 and 5, we will accept that sin 2 x = sin x sin x , which is the standard interpretation. • On the other hand (and this compounds the confusion), some sources use n to indicate the number of applications of f in compositions of f with itself; the result is called an iterated function . For example, they would let f 2 = f ± f , and they would use the rule: f 2 x = ffx . This is typically different from the rule f 2 x = ± ² ³ ´ ± ² ³ ´ . However, our use of the notation f ± 1 for “ f inverse” is more consistent with this second interpretation, since f ± 1 ± f is an identity function, which could be construed as f 0 in this context.
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This document was uploaded on 12/29/2011.

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