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Korea National Olympiad
2019 Korea National Olympiad
5
Functional Equation
Functional Equation
Source: Korea National Olympiad 2019 P5
November 16, 2019
algebra
functional equation
Problem Statement
Find all functions
f
f
f
such that
f
:
R
→
R
f:\mathbb{R}\rightarrow \mathbb{R}
f
:
R
→
R
and
f
(
f
(
x
)
−
x
+
y
2
)
=
y
f
(
y
)
f(f(x)-x+y^2)=yf(y)
f
(
f
(
x
)
−
x
+
y
2
)
=
y
f
(
y
)
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