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find real f so that f(2x + f(y)) + f(f(y)) = 4x + 8y
find real f so that f(2x + f(y)) + f(f(y)) = 4x + 8y
Source: Irmo 2018 p2 q6
September 16, 2018
algebra
functional equation
Problem Statement
Find all real-valued functions
f
f
f
satisfying
f
(
2
x
+
f
(
y
)
)
+
f
(
f
(
y
)
)
=
4
x
+
8
y
f(2x + f(y)) + f(f(y)) = 4x + 8y
f
(
2
x
+
f
(
y
))
+
f
(
f
(
y
))
=
4
x
+
8
y
for all real numbers
x
x
x
and
y
y
y
.
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