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Standard XII
Maths
Question
If
f
(
x
)
+
2
f
(
1
x
)
=
3
x
,
x
≠
0
and
S
=
{
x
∈
R
:
f
(
x
)
=
f
(
−
x
)
}
,
then
S
:
contains exactly one element.
is an empty set.
contains exactly two elements.
contains more than two elements.
A
contains exactly two elements.
B
contains more than two elements.
C
is an empty set.
D
contains exactly one element.
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Solution
Verified by Toppr
f
(
x
)
+
2
f
(
1
x
)
=
3
x
Putting
x
as
1
x
then
f
(
1
x
)
+
2
f
(
x
)
=
3
x
Solving these two equations,
f
(
x
)
=
2
x
−
x
Now for
f
(
x
)
=
f
(
−
x
)
⇒
2
x
−
x
=
x
−
2
x
⇒
2
×
2
x
=
2
x
⇒
x
2
=
2
∴
x
=
√
2
,
−
√
2
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18
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