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Baltic Way
2022 Baltic Way
5
5
Part of
2022 Baltic Way
Problems
(1)
Standart looking FE
Source: Baltic Way 2022, Problem 5
11/12/2022
Let
R
\mathbb{R}
R
be the set of real numbers. Determine all functions
f
:
R
→
R
f: \mathbb{R} \rightarrow \mathbb{R}
f
:
R
→
R
such that
f
(
0
)
+
1
=
f
(
1
)
f(0)+1=f(1)
f
(
0
)
+
1
=
f
(
1
)
and for any real numbers
x
x
x
and
y
y
y
,
f
(
x
y
−
x
)
+
f
(
x
+
f
(
y
)
)
=
y
f
(
x
)
+
3
f(xy-x)+f(x+f(y))=yf(x)+3
f
(
x
y
−
x
)
+
f
(
x
+
f
(
y
))
=
y
f
(
x
)
+
3
algebra
Baltic Way
functional equation