(Section 1.9: Inverses of One-to-One Functions) 1.9.16 2.fn. Many instructors reluctantly use the f±1notation to represent the inverse function off. • This is because noften represents an exponentin the notation fn, exceptwhen n=±1. For example, f2is often taken to mean ff; that is, f2x()=fx±²³´±²³´. In Chapters 4 and 5, we will accept that sin2x=sinxsinx, which is the standard interpretation. • On the other hand (and this compounds the confusion), some sources use nto indicate the number of applicationsoffin compositions offwith itself; the result is called an iterated function. For example, they would let f2=f±f, and they would use the rule: f2x=ffx. This is typically different from the rule f2x=±²³´±²³´. However, our use of the notation f±1for “finverse” is more consistent with this second interpretation, since f±1±fis an identity function, which could be construed as f0in this context.
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