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5
f(x+f(y)) = y+f(x+1) continuous
f(x+f(y)) = y+f(x+1) continuous
Source: Estonia IMO TST 2007 p5
March 28, 2020
functional
continuous
functional equation
algebra
Problem Statement
Find all continuous functions
f
:
R
ā
R
f: R \to R
f
:
R
ā
R
such that for all reals
x
x
x
and
y
y
y
,
f
(
x
+
f
(
y
)
)
=
y
+
f
(
x
+
1
)
f(x+f(y)) = y+f(x+1)
f
(
x
+
f
(
y
))
=
y
+
f
(
x
+
1
)
.
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