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TS EAMCET 6-Aug-2021 Shift 2 Question Paper
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Section:
Mathematics
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© examsnet.com
Question : 1
Total: 160
Mathematics
If
f
:
R
\
{
0
}
→
R
is such that
2
f
(
x
)
+
f
(
1
x
)
=
4
x
, and
S
=
{
x
∊
R
:
f
(
x
)
=
f
(
−
x
)
}
, then the number of elements in
S
is
0
1
2
at least three
Validate
Solution:
Given,
2
f
(
x
)
+
f
(
1
x
)
=
4
x
. . . (i)
Replace
x
by
1
∕
x
, we get,
2
f
(
1
∕
x
)
+
f
(
x
)
=
4
x
. . . (ii)
On multiply by 2 in Eq. (i) and then subtracting Eq. (ii), we get
4
f
(
x
)
+
2
f
(
1
x
)
=
8
x
f
(
x
)
+
2
f
(
1
∕
x
)
=
4
x
3
f
(
x
)
=
8
x
−
4
x
=
8
x
2
−
4
x
∴
f
(
x
)
=
8
x
2
−
4
3
x
=
4
(
2
x
2
−
1
)
3
x
and
f
(
−
x
)
=
4
(
2
x
2
−
1
)
−
3
x
Again given,
f
(
x
)
=
f
(
−
x
)
4
(
2
x
2
−
1
)
3
x
=
−
[
4
(
2
x
2
−
1
)
3
x
]
⇒
2
[
4
(
2
x
2
−
1
)
3
x
]
=
0
⇒
2
x
2
−
1
=
0
but
x
≠
0
⇒
x
=
±
1
√
2
but
x
≠
0
∴
S
=
(
−
1
∕
√
2
,
1
∕
√
2
}
© examsnet.com
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