MathDB
Problems
Contests
National and Regional Contests
Latvia Contests
Latvia BW TST
2022 Latvia Baltic Way TST
P3
P3
Part of
2022 Latvia Baltic Way TST
Problems
(1)
Standard looking FE
Source: Latvian TST for Baltic Way 2022 P3
10/25/2022
Let
R
\mathbb R
R
be the set of real numbers. Determine all functions
f
:
R
→
R
f:\mathbb R\to\mathbb R
f
:
R
→
R
that satisfy the equation
f
(
f
(
x
)
)
+
y
f
(
x
y
+
1
)
=
f
(
x
−
f
(
y
)
)
+
x
f
(
y
)
2
.
f(f(x))+yf(xy+1) = f(x-f(y)) + xf(y)^2.
f
(
f
(
x
))
+
y
f
(
x
y
+
1
)
=
f
(
x
−
f
(
y
))
+
x
f
(
y
)
2
.
for all real numbers
x
x
x
and
y
y
y
.
functional equation
TST