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2012 CHMMC Fall
2
2012 Fall CHMMC Tiebreaker 2 continuous f(x + f(y)) = f(x + y) + y
2012 Fall CHMMC Tiebreaker 2 continuous f(x + f(y)) = f(x + y) + y
Source:
March 1, 2024
algebra
CHMMC
functional
continuous function
Problem Statement
Find all continuous functions
f
:
R
→
R
f : R \to R
f
:
R
→
R
such that
f
(
x
+
f
(
y
)
)
=
f
(
x
+
y
)
+
y
,
f(x + f(y)) = f(x + y) + y,
f
(
x
+
f
(
y
))
=
f
(
x
+
y
)
+
y
,
for all
x
,
y
∈
R
x, y \in R
x
,
y
∈
R
. No proof is required for this problem.
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