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International Mathematical Arhimede Contest (IMAC)
2010 IMAC Arhimede
2
2
Part of
2010 IMAC Arhimede
Problems
(1)
f(x + y) = f(x) + f(y) + f(xy) , real
Source: IMAC Arhimede 2010 p2
5/5/2019
Find all functions
f
:
R
→
R
f: \mathbb{R}\to\mathbb{R}
f
:
R
→
R
such that we have
f
(
x
+
y
)
=
f
(
x
)
+
f
(
y
)
+
f
(
x
y
)
f(x + y) = f(x) + f(y) + f(xy)
f
(
x
+
y
)
=
f
(
x
)
+
f
(
y
)
+
f
(
x
y
)
for all
x
,
y
∈
R
x,y\in \mathbb{R}
x
,
y
∈
R
algebra
functional equation