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Baltic Way
2015 Baltic Way
5
5
Part of
2015 Baltic Way
Problems
(1)
Functional Equation
Source: Baltic Way 2015
11/8/2015
Find all functions
f
:
R
→
R
f:\mathbb{R}\to\mathbb{R}
f
:
R
→
R
satisfying the equation
∣
x
∣
f
(
y
)
+
y
f
(
x
)
=
f
(
x
y
)
+
f
(
x
2
)
+
f
(
f
(
y
)
)
|x|f(y)+yf(x)=f(xy)+f(x^2)+f(f(y))
∣
x
∣
f
(
y
)
+
y
f
(
x
)
=
f
(
x
y
)
+
f
(
x
2
)
+
f
(
f
(
y
))
for all real numbers
x
x
x
and
y
y
y
.
algebra
functional equation
Baltic Way