MathDB
Problems
Contests
National and Regional Contests
Kyrgyzstan Contests
Kyrgyzstan National Olympiad
2012 Kyrgyzstan National Olympiad
4
Functional Equation - $f(f(x)^2+f(y)) = xf(x)+y$
Functional Equation - $f(f(x)^2+f(y)) = xf(x)+y$
Source: Kyrgyzstan 2012, Problem 4
May 2, 2013
function
algebra
functional equation
Problem Statement
Find all functions
f
:
R
→
R
f:\mathbb{R}\to\mathbb{R}
f
:
R
→
R
such that
f
(
f
(
x
)
2
+
f
(
y
)
)
=
x
f
(
x
)
+
y
f(f(x)^2+f(y)) = xf(x)+y
f
(
f
(
x
)
2
+
f
(
y
))
=
x
f
(
x
)
+
y
,
∀
x
,
y
∈
R
\forall x,y\in R
∀
x
,
y
∈
R
.
Back to Problems
View on AoPS