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Ukraine Contests
Official Ukraine Selection Cycle
Ukraine Team Selection Test
1999 Ukraine Team Selection Test
9
9
Part of
1999 Ukraine Team Selection Test
Problems
(1)
f(x+y) = f(x)u(y)+ f(y) , strictly increasing function f : R \to R
Source: Ukrainian TST 1999 p9
2/13/2020
Find all functions
u
:
R
→
R
u : R \to R
u
:
R
→
R
for which there is a strictly increasing function
f
:
R
→
R
f : R \to R
f
:
R
→
R
such that
f
(
x
+
y
)
=
f
(
x
)
u
(
y
)
+
f
(
y
)
f(x+y) = f(x)u(y)+ f(y)
f
(
x
+
y
)
=
f
(
x
)
u
(
y
)
+
f
(
y
)
for all
x
,
y
∈
R
x,y \in R
x
,
y
∈
R
.
function
functional equation
algebra