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Baltic Way
2017 Baltic Way
5
Functional Equation
Functional Equation
Source: Baltic Way 2017 Problem 5
November 14, 2017
algebra
functional equation
easy functional equation
Baltic Way
Problem Statement
Find all functions
f
:
R
ā
R
f:\mathbb{R}\rightarrow\mathbb{R}
f
:
R
ā
R
such that
f
(
x
2
y
)
=
f
(
x
y
)
+
y
f
(
f
(
x
)
+
y
)
f(x^2y)=f(xy)+yf(f(x)+y)
f
(
x
2
y
)
=
f
(
x
y
)
+
y
f
(
f
(
x
)
+
y
)
for all real numbers
x
x
x
and
y
y
y
.
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