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Flanders Math Olympiad
2002 Flanders Math Olympiad
2
easy functional equitation (Flanders '02)
easy functional equitation (Flanders '02)
Source:
August 8, 2004
function
Problem Statement
Determine all functions
f
:
R
→
R
f: \mathbb{R}\rightarrow\mathbb{R}
f
:
R
→
R
so that
∀
x
:
x
⋅
f
(
x
2
)
−
f
(
2
x
)
=
1
\forall x: x\cdot f(\frac x2) - f(\frac2x) = 1
∀
x
:
x
⋅
f
(
2
x
)
−
f
(
x
2
)
=
1
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