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1969 IMO Shortlist
8
8
Part of
1969 IMO Shortlist
Problems
(1)
xf(y)+yf(x)=(x+y)f(x)f(y) - ILL BUL2
Source: ILL BUL2
9/29/2010
Find all functions
f
f
f
defined for all
x
x
x
that satisfy the condition
x
f
(
y
)
+
y
f
(
x
)
=
(
x
+
y
)
f
(
x
)
f
(
y
)
,
xf(y) + yf(x) = (x + y)f(x)f(y),
x
f
(
y
)
+
y
f
(
x
)
=
(
x
+
y
)
f
(
x
)
f
(
y
)
,
for all
x
x
x
and
y
.
y.
y
.
Prove that exactly two of them are continuous.
function
algebra
functional equation
continuous function
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