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Azerbaijan Contests
Azerbaijan IZHO TST
2020 Azerbaijan IZHO TST
3
3
Part of
2020 Azerbaijan IZHO TST
Problems
(1)
Function problem
Source: Azerbaijan Math Olympiad Training
12/15/2019
Find all functions
u
:
R
→
R
u:R\rightarrow{R}
u
:
R
→
R
for which there exists a strictly monotonic function
f
:
R
→
R
f:R\rightarrow{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{\mathbb{R}}
x
,
y
∈
R
algebra
functional equation
TST