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2017 239 Open Mathematical Olympiad
3
(y+1)f(yf(x))=yf(x(y+1))
(y+1)f(yf(x))=yf(x(y+1))
Source: 239 2017 S3
May 22, 2020
functional equation
Functional equation in R
algebra
TuZo cheating
Problem Statement
Find all functions
f
:
R
ā
R
f: \mathbb{R} \to \mathbb{R}
f
:
R
ā
R
such that for all real number
x
,
y
x,y
x
,
y
,
(
y
+
1
)
f
(
y
f
(
x
)
)
=
y
f
(
x
(
y
+
1
)
)
.
(y+1)f(yf(x))=yf(x(y+1)).
(
y
+
1
)
f
(
y
f
(
x
))
=
y
f
(
x
(
y
+
1
))
.
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