MathDB
Problems
Contests
National and Regional Contests
India Contests
India IMO Training Camp
2003 India IMO Training Camp
3
3
Part of
2003 India IMO Training Camp
Problems
(1)
Find f if f(x+y)+f(x)f(y)=f(xy)+f(x)+f(y)
Source:
1/9/2011
Find all functions
f
:
R
ā
R
f: \mathbb R \to \mathbb R
f
:
R
ā
R
such that for all reals
x
x
x
and
y
y
y
,
f
(
x
+
y
)
+
f
(
x
)
f
(
y
)
=
f
(
x
y
)
+
f
(
x
)
+
f
(
y
)
.
f(x+y)+f(x)f(y)=f(xy)+f(x)+f(y).
f
(
x
+
y
)
+
f
(
x
)
f
(
y
)
=
f
(
x
y
)
+
f
(
x
)
+
f
(
y
)
.
function
algebra proposed
algebra