MathDB
Problems
Contests
National and Regional Contests
Serbia Contests
Serbia National Math Olympiad
2021 Serbia National Math Olympiad
5
5
Part of
2021 Serbia National Math Olympiad
Problems
(1)
Functional equation
Source: Serbian Mathematical Olympiad 2021, P5
5/14/2021
Find all functions
f
:
R
→
R
f:\mathbb{R}\rightarrow\mathbb{R}
f
:
R
→
R
such that for every
x
,
y
∈
R
x,y\in\mathbb{R}
x
,
y
∈
R
the following equality holds:
f
(
x
f
(
y
)
+
x
2
+
y
)
=
f
(
x
)
f
(
y
)
+
x
f
(
x
)
+
f
(
y
)
.
f(xf(y)+x^2+y)=f(x)f(y)+xf(x)+f(y).
f
(
x
f
(
y
)
+
x
2
+
y
)
=
f
(
x
)
f
(
y
)
+
x
f
(
x
)
+
f
(
y
)
.
functional equation
function
algebra