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Problems
Contests
National and Regional Contests
Azerbaijan Contests
Azerbaijan BMO TST
2022 Azerbaijan BMO TST
2022 Azerbaijan BMO TST
Part of
Azerbaijan BMO TST
Subcontests
(1)
A2
1
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f (x + yf(x + y))= y^2 + f(x)f(y)
Find all functions
f
:
R
→
R
f : R \to R
f
:
R
→
R
with
f
(
x
+
y
f
(
x
+
y
)
)
=
y
2
+
f
(
x
)
f
(
y
)
f (x + yf(x + y))= y^2 + f(x)f(y)
f
(
x
+
y
f
(
x
+
y
))
=
y
2
+
f
(
x
)
f
(
y
)
for all
x
,
y
∈
R
x, y \in R
x
,
y
∈
R
.