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Baltic Way
2019 Baltic Way
3
Boring Functional Equation
Boring Functional Equation
Source: 2019 Baltic Way P3
November 18, 2019
algebra
functional equation
Baltic Way
Problem Statement
Find all functions
f
:
R
→
R
f:\mathbb{R}\to\mathbb{R}
f
:
R
→
R
such that
f
(
x
f
(
y
)
−
y
2
)
=
(
y
+
1
)
f
(
x
−
y
)
f(xf(y)-y^2)=(y+1)f(x-y)
f
(
x
f
(
y
)
−
y
2
)
=
(
y
+
1
)
f
(
x
−
y
)
holds for all
x
,
y
∈
R
x,y\in\mathbb{R}
x
,
y
∈
R
.
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