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2017 Pan-African Shortlist
A4
f ( f (x)+y) = f (x^2 -y)+4 f (x)y
f ( f (x)+y) = f (x^2 -y)+4 f (x)y
Source: Czech and Slovak Match 1997 P3
October 1, 2017
functional equation
algebra
Problem Statement
Find all functions
f
:
R
→
R
f : R\rightarrow R
f
:
R
→
R
such that
f
(
f
(
x
)
+
y
)
=
f
(
x
2
−
y
)
+
4
f
(
x
)
y
f ( f (x)+y) = f (x^2 -y)+4 f (x)y
f
(
f
(
x
)
+
y
)
=
f
(
x
2
−
y
)
+
4
f
(
x
)
y
for all
x
,
y
∈
R
x,y \in R
x
,
y
∈
R
.
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