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(Section 1.9: Inverses of OnetoOne 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.
 Spring '09

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