MathDB
Problems
Contests
National and Regional Contests
India Contests
India National Olympiad
2011 India National Olympiad
6
Functional equation from R to R-[INMO 2011]
Functional equation from R to R-[INMO 2011]
Source:
February 6, 2011
function
algebra
functional equation
algebra proposed
Problem Statement
Find all functions
f
:
R
→
R
f:\mathbb{R}\to \mathbb R
f
:
R
→
R
satisfying
f
(
x
+
y
)
f
(
x
−
y
)
=
(
f
(
x
)
+
f
(
y
)
)
2
−
4
x
2
f
(
y
)
,
f(x+y)f(x-y)=\left(f(x)+f(y)\right)^2-4x^2f(y),
f
(
x
+
y
)
f
(
x
−
y
)
=
(
f
(
x
)
+
f
(
y
)
)
2
−
4
x
2
f
(
y
)
,
For all
x
,
y
∈
R
x,y\in\mathbb R
x
,
y
∈
R
.
Back to Problems
View on AoPS