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Contests
National and Regional Contests
Belgium Contests
Flanders Math Olympiad
1999 Flanders Math Olympiad
3
functional equation (flanders '99)
functional equation (flanders '99)
Source:
August 30, 2004
quadratics
Problem Statement
Determine all
f
:
R
→
R
f: \mathbb{R}\rightarrow\mathbb{R}
f
:
R
→
R
for which
2
⋅
f
(
x
)
−
g
(
x
)
=
f
(
y
)
−
y
and
f
(
x
)
⋅
g
(
x
)
≥
x
+
1.
2\cdot f(x)-g(x)=f(y)-y \textrm{ and } f(x)\cdot g(x) \geq x+1.
2
⋅
f
(
x
)
−
g
(
x
)
=
f
(
y
)
−
y
and
f
(
x
)
⋅
g
(
x
)
≥
x
+
1.
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