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Danube Competition in Mathematics
2019 Danube Mathematical Competition
2
f(f(x²)+y+f(y))=x²+2f(y)
f(f(x²)+y+f(y))=x²+2f(y)
Source: 2019 Danube
October 29, 2019
function
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algebra
functional equation
Problem Statement
Find all nondecreasing functions
f
:
R
⟶
R
f:\mathbb{R}\longrightarrow\mathbb{R}
f
:
R
⟶
R
that verify the relation
f
(
f
(
x
2
)
+
y
+
f
(
y
)
)
=
x
2
+
2
f
(
y
)
,
f\left( f\left( x^2 \right) +y+f(y) \right) =x^2+2f(y) ,
f
(
f
(
x
2
)
+
y
+
f
(
y
)
)
=
x
2
+
2
f
(
y
)
,
for any real numbers
x
,
y
.
x,y.
x
,
y
.
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