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(Section 1.9: Inverses of One-to-One Functions)
1.9.2
PART B: INVERSE FUNCTIONS
We will begin by reviewing additive and multiplicative inverses.
• 0 is the
additive identity
of
±
, because, if we add 0 to any real number, the
result is identical to that number. Similarly, 1 is the
multiplicative identity
.
• The
additive inverse
of, say, the real number 3 is
±
3
. That is,
±
3
is the inverse
of 3 with respect to
addition
. This is because, if the two numbers are added, the
result is the
additive identity
, 0.
• The
multiplicative inverse
(or
reciprocal
) of 3 is
1
3
. That is,
1
3
is the inverse of
3 with respect to
multiplication
. This is because, if the two numbers are
multiplied, the result is the
multiplicative identity
, 1.
A pair of inverse functions
have the property that, when they are
composed
in
either order, the result is the
identity

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