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India National Olympiad
1992 India National Olympiad
10
Functional eqn.
Functional eqn.
Source: INMO 1992 Problem 10
October 4, 2005
function
Problem Statement
Determine all functions
f
:
R
−
[
0
,
1
]
→
R
f : \mathbb{R} - [0,1] \to \mathbb{R}
f
:
R
−
[
0
,
1
]
→
R
such that
f
(
x
)
+
f
(
1
1
−
x
)
=
2
(
1
−
2
x
)
x
(
1
−
x
)
.
f(x) + f \left( \dfrac{1}{1-x} \right) = \dfrac{2(1-2x)}{x(1-x)} .
f
(
x
)
+
f
(
1
−
x
1
)
=
x
(
1
−
x
)
2
(
1
−
2
x
)
.
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