MathDB
Problems
Contests
National and Regional Contests
India Contests
India IMO Training Camp
2010 India IMO Training Camp
11
11
Part of
2010 India IMO Training Camp
Problems
(1)
Indian Team Selection Test 2010 ST4 P2
Source:
5/23/2010
Find all functions
f
:
R
⟶
R
f:\mathbb{R}\longrightarrow\mathbb{R}
f
:
R
⟶
R
such that
f
(
x
+
y
)
+
x
y
=
f
(
x
)
f
(
y
)
f(x+y)+xy=f(x)f(y)
f
(
x
+
y
)
+
x
y
=
f
(
x
)
f
(
y
)
for all reals
x
,
y
x, y
x
,
y
function
algebra proposed
algebra