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2
Function on real
Function on real
Source: Moldova TST 2014, Third Day, Problem 2
March 31, 2014
function
algebra proposed
algebra
Problem Statement
Find all functions
f
:
R
→
R
f:R \rightarrow R
f
:
R
→
R
, which satisfy the equality for any
x
,
y
∈
R
x,y \in R
x
,
y
∈
R
:
f
(
x
f
(
y
)
+
y
)
+
f
(
x
y
+
x
)
=
f
(
x
+
y
)
+
2
x
y
f(xf(y)+y)+f(xy+x)=f(x+y)+2xy
f
(
x
f
(
y
)
+
y
)
+
f
(
x
y
+
x
)
=
f
(
x
+
y
)
+
2
x
y
,
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