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2018-IMOC
A3
f(xf(y)+y)=yf(x)+f(y) over R
f(xf(y)+y)=yf(x)+f(y) over R
Source: IMOC 2018 A3
August 15, 2021
fe
functional equation
algebra
Problem Statement
Find all functions
f
:
R
ā
R
f:\mathbb R\to\mathbb R
f
:
R
ā
R
such that for reals
x
,
y
x,y
x
,
y
,
f
(
x
f
(
y
)
+
y
)
=
y
f
(
x
)
+
f
(
y
)
.
f(xf(y)+y)=yf(x)+f(y).
f
(
x
f
(
y
)
+
y
)
=
y
f
(
x
)
+
f
(
y
)
.
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