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JEE Advanced 2012 Paper 2 Mathematics Q12
Mathematics
Problem
Consider the statements:
P
\mathbf P
P
: There exists some
x
∈
R
x\in\mathbb R
x
∈
R
such that
f
(
x
)
+
2
x
=
2
(
1
+
x
2
)
f(x)+2x=2(1+x^2)
f
(
x
)
+
2
x
=
2
(
1
+
x
2
)
.
Q
\mathbf Q
Q
: There exists some
x
∈
R
x\in\mathbb R
x
∈
R
such that
2
f
(
x
)
+
1
=
2
x
(
1
+
x
)
2f(x)+1=2x(1+x)
2
f
(
x
)
+
1
=
2
x
(
1
+
x
)
. Then
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