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C01S03.017:
The domain of
f
(
x
)=
x
√
x
+ 2 is the interval [
−
2
,
+
∞
), so its graph must be the one
shown in Fig. 1.3.38.
C01S03.018:
The domain of
f
(
x
)=
√
2
x
−
x
2
consists of those numbers for which 2
x
−
x
2
=
0; that is,
x
(2
−
x
)
=
0. This occurs when
x
and 2
−
x
have the same sign and also when either is zero. If
x>
0 and
2
−
x>
0, then 0
<x<
2. If
x<
0 and 2
−
x<
0, then
x<
0 and
x>
2, which is impossible. Hence the
domain of
f
is the closed interval [0
,
2]. So the graph of
f
must be the one shown in Fig. 1.3.36.
C01S03.019:
The domain of
f
(
x
)=
√
x
2
−
2
x
consists of those numbers
x
for which
x
2
−
2
x
=
0; that
is,
x
(
x
−
2)
=
0. This occurs when
x
and
x
−
2 have the same sign and also when either is zero. If
x>
0
and
x
−
2
>
0, then
x>
2; if
x<
0 and
x
−
2
<
0, then
x<
0. So the domain of
f
is the union of the two
intervals (
−∞
,
0] and [2
,
+
∞
). So the graph of
f
must be the one shown in Fig. 1.3.39.
C01S03.020:
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This note was uploaded on 09/14/2011 for the course MATH 101 taught by Professor Cheng during the Spring '11 term at Ecole Hôtelière de Lausanne.
 Spring '11
 CHENG
 Calculus

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