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National and Regional Contests
Malaysia Contests
Malaysian IMO Training Camp
BIMO 2020
1
1
Part of
BIMO 2020
Problems
(1)
f(x^2+f(x+y))=y+xf(x+1)
Source: Own. IMO 2020 Malaysian Final Training
1/29/2022
Find all functions
f
:
R
ā
R
f : \mathbb{R} \rightarrow \mathbb{R}
f
:
R
ā
R
such that for all reals
x
,
y
x, y
x
,
y
,
f
(
x
2
+
f
(
x
+
y
)
)
=
y
+
x
f
(
x
+
1
)
f(x^2+f(x+y))=y+xf(x+1)
f
(
x
2
+
f
(
x
+
y
))
=
y
+
x
f
(
x
+
1
)
algebra
functional equation