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Flanders Math Olympiad
2006 Flanders Math Olympiad
4
Functional equation
Functional equation
Source: Flanders MO 2006 Q4
April 19, 2006
function
calculus
algebra
functional equation
system of equations
Problem Statement
Find all functions
f
:
R
\
{
0
,
1
}
→
R
f: \mathbb{R}\backslash\{0,1\} \rightarrow \mathbb{R}
f
:
R
\
{
0
,
1
}
→
R
such that
f
(
x
)
+
f
(
1
1
−
x
)
=
1
+
1
x
(
1
−
x
)
.
f(x)+f\left(\frac{1}{1-x}\right) = 1+\frac{1}{x(1-x)}.
f
(
x
)
+
f
(
1
−
x
1
)
=
1
+
x
(
1
−
x
)
1
.
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