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Switzerland Team Selection Test
2000 Switzerland Team Selection Test
12
f(f(x)+y) = f(x^2 -y)+4y f(x)
f(f(x)+y) = f(x^2 -y)+4y f(x)
Source: Switzerland - Swiss TST 2000 p12
February 19, 2020
functional equation
functional
algebra
Problem Statement
Find all functions
f
:
R
→
R
f : R \to R
f
:
R
→
R
such that for all real
x
,
y
x,y
x
,
y
,
f
(
f
(
x
)
+
y
)
=
f
(
x
2
−
y
)
+
4
y
f
(
x
)
f(f(x)+y) = f(x^2 -y)+4y f(x)
f
(
f
(
x
)
+
y
)
=
f
(
x
2
−
y
)
+
4
y
f
(
x
)
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