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International Zhautykov Olympiad
2017 International Zhautykov Olympiad
2
IZHO 2017 Functional equations
IZHO 2017 Functional equations
Source: IZHO 2017 Day 1 Problem 2
January 14, 2017
functional equation
function
algebra
Problem Statement
Find all functions
f
:
R
→
R
f:R \rightarrow R
f
:
R
→
R
such that
(
x
+
y
2
)
f
(
y
f
(
x
)
)
=
x
y
f
(
y
2
+
f
(
x
)
)
(x+y^2)f(yf(x))=xyf(y^2+f(x))
(
x
+
y
2
)
f
(
y
f
(
x
))
=
x
y
f
(
y
2
+
f
(
x
))
, where
x
,
y
∈
R
x,y \in \mathbb{R}
x
,
y
∈
R
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