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Malaysian IMO Training Camp
BIMO 2022
1
f(xf(x)+2y)=f(x)^2+x+2f(y)
f(xf(x)+2y)=f(x)^2+x+2f(y)
Source: Own. IMO 2022 Malaysian Training Camp 1
January 29, 2022
algebra
functional equation
Problem Statement
Find all functions
f
:
R
ā
R
f:\mathbb{R}\rightarrow \mathbb{R}
f
:
R
ā
R
such that for all real numbers
x
,
y
x,y
x
,
y
, we have
f
(
x
f
(
x
)
+
2
y
)
=
f
(
x
)
2
+
x
+
2
f
(
y
)
f(xf(x)+2y)=f(x)^2+x+2f(y)
f
(
x
f
(
x
)
+
2
y
)
=
f
(
x
)
2
+
x
+
2
f
(
y
)
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