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1987 Flanders Math Olympiad
3
[to be solved] - functional equation
[to be solved] - functional equation
Source: flanders '87
August 9, 2004
function
AMC
USA(J)MO
USAMO
Problem Statement
Find all continuous functions
f
:
R
→
R
f: \mathbb{R}\rightarrow\mathbb{R}
f
:
R
→
R
such that
f
(
x
)
3
=
−
x
12
⋅
(
x
2
+
7
x
⋅
f
(
x
)
+
16
⋅
f
(
x
)
2
)
,
∀
x
∈
R
.
f(x)^3 = -\frac x{12}\cdot\left(x^2+7x\cdot f(x)+16\cdot f(x)^2\right),\ \forall x \in \mathbb{R}.
f
(
x
)
3
=
−
12
x
⋅
(
x
2
+
7
x
⋅
f
(
x
)
+
16
⋅
f
(
x
)
2
)
,
∀
x
∈
R
.
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