MathDB
Problems
Contests
National and Regional Contests
Nepal Contests
Nepal TST
2019 Nepal TST
P3
P3
Part of
2019 Nepal TST
Problems
(1)
NEPAL TST 2019
Source:
5/14/2019
Find all functions
f
:
R
ā
R
f : \mathbb{R} \to \mathbb{R}
f
:
R
ā
R
such that for any real
x
,
y
x, y
x
,
y
holds equality
f
(
x
f
(
y
)
)
+
f
(
x
y
)
=
2
f
(
x
)
y
f(xf(y)) + f(xy) = 2f(x)y
f
(
x
f
(
y
))
+
f
(
x
y
)
=
2
f
(
x
)
y
Proposed by Arseniy Nikolaev
algebra