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(Section 1.9: Inverses of OnetoOne Functions)
1.9.6
Example 3 (A Function that is Not OnetoOne: Unrestricted Squaring Function)
Let
fx
()
=
x
2
on
±
. Then,
f
is a function, but it is
not
onetoone on
±
, as
demonstrated by the figures below:
InputOutput Machine
Partial Arrow Diagram
Graph
Fails HLT (Section 1.8)
§
• Also,
fa
=
fc
±
a
2
=
c
2
±
a
=±
c
, which is
not
equivalent to
a
=
c
, if
c
±
0
.
If we
solve the equation
=
9
, or
x
2
=
9
, we obtain
two
solutions for
x
,
namely
3 and
±
3
. These are the
two
answers to the question, “Whose square
is 9?”
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This document was uploaded on 12/29/2011.
 Spring '09

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