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National and Regional Contests
India Contests
Postal Coaching
2005 Postal Coaching
19
Func eqn
Func eqn
Source: Indian Postal Coaching 2005
October 27, 2005
function
algebra
polynomial
Problem Statement
Find all functions
f
:
R
↦
R
f : \mathbb{R} \mapsto \mathbb{R}
f
:
R
↦
R
such that
f
(
x
y
+
f
(
x
)
)
=
x
f
(
y
)
+
f
(
x
)
f(xy+f(x)) = xf(y) +f(x)
f
(
x
y
+
f
(
x
))
=
x
f
(
y
)
+
f
(
x
)
for all
x
,
y
∈
R
x,y \in \mathbb{R}
x
,
y
∈
R
.
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