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Functional Equation
Functional Equation
Source: Azerbaijan IMO TST 2016,D2 P3
May 26, 2018
function
functional equation
algebra
Problem Statement
Prove that there does not exist a function
f
:
R
+
ā
R
+
f : \mathbb R^+\to\mathbb R^+
f
:
R
+
ā
R
+
such that
f
(
f
(
x
)
+
y
)
=
f
(
x
)
+
3
x
+
y
f
(
y
)
f(f(x)+y)=f(x)+3x+yf(y)
f
(
f
(
x
)
+
y
)
=
f
(
x
)
+
3
x
+
y
f
(
y
)
for all positive reals
x
,
y
x,y
x
,
y
.
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