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Standard XII
Mathematics
Question
Let
f
:
(
0
,
∞
)
→
R
be given by
f
(
x
)
=
∫
x
1
/
x
e
(
t
+
1
t
)
d
t
t
, then
f
(
x
)
is monotonically increasing on
[
1
,
∞
)
f
(
x
)
is monotonically decreasing on (0, 1)
f
(
x
)
+
f
(
1
x
)
=
0
, for all
x
∈
(
0
,
∞
)
f
(
2
x
)
is an odd function of x on R
A
f
(
x
)
is monotonically increasing on
[
1
,
∞
)
B
f
(
x
)
+
f
(
1
x
)
=
0
, for all
x
∈
(
0
,
∞
)
C
f
(
x
)
is monotonically decreasing on (0, 1)
D
f
(
2
x
)
is an odd function of x on R
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