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Indonesia TST
2012 Indonesia TST
1
Functional equation
Functional equation
Source: 2012 Indonesia Round 2 TST 3 Problem 1
March 18, 2012
function
algebra unsolved
algebra
Problem Statement
Find all functions
f
:
R
→
R
f : \mathbb{R} \rightarrow \mathbb{R}
f
:
R
→
R
such that
f
(
x
+
y
)
+
f
(
x
)
f
(
y
)
=
f
(
x
y
)
+
(
y
+
1
)
f
(
x
)
+
(
x
+
1
)
f
(
y
)
f(x+y) + f(x)f(y) = f(xy) + (y+1)f(x) + (x+1)f(y)
f
(
x
+
y
)
+
f
(
x
)
f
(
y
)
=
f
(
x
y
)
+
(
y
+
1
)
f
(
x
)
+
(
x
+
1
)
f
(
y
)
for all
x
,
y
∈
R
x,y \in \mathbb{R}
x
,
y
∈
R
.
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