MathDB
Problems
Contests
National and Regional Contests
Latvia Contests
Latvia BW TST
2019 Latvia Baltic Way TST
2
2
Part of
2019 Latvia Baltic Way TST
Problems
(1)
Easy, classical FE
Source: Latvian TST for Baltic Way 2019 Problem 2
5/29/2020
Let
R
\mathbb R
R
be set of real numbers. Determine all functions
f
:
R
→
R
f:\mathbb R\to \mathbb R
f
:
R
→
R
such that
f
(
y
2
−
f
(
x
)
)
=
y
f
(
x
)
2
+
f
(
x
2
y
+
y
)
f(y^2 - f(x)) = yf(x)^2+f(x^2y+y)
f
(
y
2
−
f
(
x
))
=
y
f
(
x
)
2
+
f
(
x
2
y
+
y
)
holds for all real numbers
x
;
y
x; y
x
;
y
function
functional equation
algebra