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Brazil National Olympiad
2006 Brazil National Olympiad
3
3
Part of
2006 Brazil National Olympiad
Problems
(1)
Yet another (but nice!) functional equation
Source: Brazilian Math Olympiad 2006, Problem 3
10/30/2006
Find all functions
f
:
R
→
R
f\colon \mathbb{R}\to \mathbb{R}
f
:
R
→
R
such that
f
(
x
f
(
y
)
+
f
(
x
)
)
=
2
f
(
x
)
+
x
y
f(xf(y)+f(x)) = 2f(x)+xy
f
(
x
f
(
y
)
+
f
(
x
))
=
2
f
(
x
)
+
x
y
for every reals
x
,
y
x,y
x
,
y
.
function
induction
algebra
functional equation
algebra unsolved