MathDB
Problems
Contests
International Contests
Baltic Way
2013 Baltic Way
3
Functional Equation
Functional Equation
Source: 2013 Baltic Way, Problem 3
December 30, 2013
function
algebra unsolved
algebra
Problem Statement
Let
R
\mathbb{R}
R
denote the set of real numbers. Find all functions
f
:
R
→
R
f:\mathbb{R}\rightarrow\mathbb{R}
f
:
R
→
R
such that
f
(
x
f
(
y
)
+
y
)
+
f
(
−
f
(
x
)
)
=
f
(
y
f
(
x
)
−
y
)
+
y
f(xf(y)+y)+f(-f(x))=f(yf(x)-y)+y
f
(
x
f
(
y
)
+
y
)
+
f
(
−
f
(
x
))
=
f
(
y
f
(
x
)
−
y
)
+
y
for all
x
,
y
∈
R
x,y\in\mathbb{R}
x
,
y
∈
R
Back to Problems
View on AoPS