MathDB
Problems
Contests
National and Regional Contests
India Contests
India National Olympiad
2001 India National Olympiad
6
6
Part of
2001 India National Olympiad
Problems
(1)
All functions f with f(x +y) = f(x) f(y) f(xy)
Source: INMO 2001 Probelm 6
10/10/2005
Find all functions
f
:
R
→
R
f : \mathbb{R} \to\mathbb{R}
f
:
R
→
R
such that
f
(
x
+
y
)
=
f
(
x
)
f
(
y
)
f
(
x
y
)
f(x +y) = f(x) f(y) f(xy)
f
(
x
+
y
)
=
f
(
x
)
f
(
y
)
f
(
x
y
)
for all
x
,
y
∈
R
.
x, y \in \mathbb{R}.
x
,
y
∈
R
.
function
algebra unsolved
algebra