MathDB
Problems
Contests
International Contests
Rioplatense Mathematical Olympiad, Level 3
2019 Rioplatense Mathematical Olympiad, Level 3
2
Rio function
Rio function
Source: Rioplatense Olympiad L3 2019
December 10, 2019
algebra
function
Problem Statement
Find all functions
f
:
R
→
R
f:\mathbb{R}\rightarrow \mathbb{R}
f
:
R
→
R
such that
f
(
f
(
x
)
2
+
f
(
y
2
)
)
=
(
x
−
y
)
f
(
x
−
f
(
y
)
)
f(f(x)^2+f(y^2))=(x-y)f(x-f(y))
f
(
f
(
x
)
2
+
f
(
y
2
))
=
(
x
−
y
)
f
(
x
−
f
(
y
))
Back to Problems
View on AoPS