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2020 IberoAmerican
5
Quality FE
Quality FE
Source: 2020 Iberoamerican #5
November 17, 2020
algebra
functional equation
Iberoamerican
Problem Statement
Determine all functions
f
:
R
→
R
f: \mathbb{R} \rightarrow \mathbb{R}
f
:
R
→
R
such that
f
(
x
f
(
x
−
y
)
)
+
y
f
(
x
)
=
x
+
y
+
f
(
x
2
)
,
f(xf(x-y))+yf(x)=x+y+f(x^2),
f
(
x
f
(
x
−
y
))
+
y
f
(
x
)
=
x
+
y
+
f
(
x
2
)
,
for all real numbers
x
x
x
and
y
.
y.
y
.
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