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Middle European Mathematical Olympiad
2024 Middle European Mathematical Olympiad
2
Another good old two-variable functional equation on R
Another good old two-variable functional equation on R
Source: MEMO 2024 T2
August 27, 2024
function
algebra
functional equation
Problem Statement
Find all functions
f
:
R
→
R
f:\mathbb{R} \to \mathbb{R}
f
:
R
→
R
such that
y
f
(
x
+
1
)
=
f
(
x
+
y
−
f
(
x
)
)
+
f
(
x
)
f
(
f
(
y
)
)
yf(x+1)=f(x+y-f(x))+f(x)f(f(y))
y
f
(
x
+
1
)
=
f
(
x
+
y
−
f
(
x
))
+
f
(
x
)
f
(
f
(
y
))
for all
x
,
y
∈
R
x,y \in \mathbb{R}
x
,
y
∈
R
.
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