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Kosovo Team Selection Test
2020 Kosovo Team Selection Test
1
1
Part of
2020 Kosovo Team Selection Test
Problems
(1)
f(x+yf(x+y))=y^2+f(x)f(y)
Source: Kosovo TST 2020 Problem 1
2/8/2020
Find all functions
f
:
R
ā
R
f:\mathbb{R}\rightarrow\mathbb{R}
f
:
R
ā
R
such that, for all real numbers
x
x
x
and
y
y
y
satisfy,
f
(
x
+
y
f
(
x
+
y
)
)
=
y
2
+
f
(
x
)
f
(
y
)
f\left(x+yf(x+y)\right)=y^2+f(x)f(y)
f
(
x
+
y
f
(
x
+
y
)
)
=
y
2
+
f
(
x
)
f
(
y
)
Proposed by Dorlir Ahmeti, Kosovo
functional equation
function
algebra