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2024 Turkey Team Selection Test
2
Easy function in turkey TST
Easy function in turkey TST
Source: 2024 Turkey TST P2
March 18, 2024
function
functional equation
Problem Statement
Find all
f
:
R
ā
R
f:\mathbb{R}\to\mathbb{R}
f
:
R
ā
R
functions such that
f
(
x
+
y
)
3
=
(
x
+
2
y
)
f
(
x
2
)
+
f
(
f
(
y
)
)
(
x
2
+
3
x
y
+
y
2
)
f(x+y)^3=(x+2y)f(x^2)+f(f(y))(x^2+3xy+y^2)
f
(
x
+
y
)
3
=
(
x
+
2
y
)
f
(
x
2
)
+
f
(
f
(
y
))
(
x
2
+
3
x
y
+
y
2
)
for all real numbers
x
,
y
x,y
x
,
y
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