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International Contests
Austrian-Polish
1988 Austrian-Polish Competition
4
4
Part of
1988 Austrian-Polish Competition
Problems
(1)
f (f(x) + y) = f(x + y) + f (0), stricly increasing
Source: Austrian Polish 1988 APMC
4/30/2020
Determine all strictly increasing functions
f
:
R
→
R
f: R \to R
f
:
R
→
R
satisfying
f
(
f
(
x
)
+
y
)
=
f
(
x
+
y
)
+
f
(
0
)
f (f(x) + y) = f(x + y) + f (0)
f
(
f
(
x
)
+
y
)
=
f
(
x
+
y
)
+
f
(
0
)
for all
x
,
y
∈
R
x,y \in R
x
,
y
∈
R
.
functional
functional equation
Increasing
algebra