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55.
[
2
5, 5] by [
2
2, 5]
We require
x
2
2
4
$
0 (so that the square root is defined)
and
x
2
2
4
±
0 (to avoid division by zero), so the domain
is (
2‘
,
2
2)
<
(2,
‘
). For values of
x
in the domain,
x
2
2
4
1
and hence
ˇ
x
2
w
2
w
4
w
and
}
ˇ
x
2
w
1
2
w
4
w
}
2
can attain any positive
value, so the range is (0,
‘
). (Note that grapher failure may
cause the range to appear as a finite interval on a
grapher.
56.
[
2
5, 5] by [
2
2, 5]
We require 9
2
x
2
$
0 (so that the fourth root is defined)
and 9
2
x
2
±
0 (to avoid division by zero), so the domain
is (
2
3, 3). For values of
x
in the domain, 9
2
x
2
can attain
any value in (0, 9]. Therefore,
ˇ
4
9
w
2
w
x
w
2
w
can attain any
value in (0,
ˇ
3
w
], and
}
ˇ
4
9
w
2
2
w
x
w
2
w
}
can attain any value in
3
}
ˇ
2
3
w
}
,
‘
2
. The range is
3
}
ˇ
2
3
w
}
,
‘
2
or approximately [1.15,
‘
).
(Note that grapher failure may cause the range to appear as
a finite interval on a grapher.)
57.
[
2
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This note was uploaded on 10/05/2011 for the course MAC 1147 taught by Professor German during the Spring '08 term at University of Florida.
 Spring '08
 GERMAN

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