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Vojtěch Jarník IMC
2008 VJIMC
Problem 2
recurrence relation, f(f(f(x)))+4f(f(x))+f(x)=6x
recurrence relation, f(f(f(x)))+4f(f(x))+f(x)=6x
Source: VJIMC 2008 1.2
June 16, 2021
fe
functional equation
Sequences
recurrence relation
algebra
Problem Statement
Find all functions
f
:
(
0
,
∞
)
→
(
0
,
∞
)
f:(0,\infty)\to(0,\infty)
f
:
(
0
,
∞
)
→
(
0
,
∞
)
such that
f
(
f
(
f
(
x
)
)
)
+
4
f
(
f
(
x
)
)
+
f
(
x
)
=
6
x
.
f(f(f(x)))+4f(f(x))+f(x)=6x.
f
(
f
(
f
(
x
)))
+
4
f
(
f
(
x
))
+
f
(
x
)
=
6
x
.
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