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Problems
Contests
National and Regional Contests
Sweden Contests
Swedish Mathematical Competition
1966 Swedish Mathematical Competition
4
4
Part of
1966 Swedish Mathematical Competition
Problems
(1)
solutions of x = f_n(x), composition, f(x) = 1 + 2/x
Source: 1966 Swedish Mathematical Competition p4
3/21/2021
Let
f
(
x
)
=
1
+
2
x
f(x) = 1 + \frac{2}{x}
f
(
x
)
=
1
+
x
2
. Put
f
1
(
x
)
=
f
(
x
)
f_1(x) = f(x)
f
1
(
x
)
=
f
(
x
)
,
f
2
(
x
)
=
f
(
f
1
(
x
)
)
f_2(x) = f(f_1(x))
f
2
(
x
)
=
f
(
f
1
(
x
))
,
f
3
(
x
)
=
f
(
f
2
(
x
)
)
f_3(x) = f(f_2(x))
f
3
(
x
)
=
f
(
f
2
(
x
))
,
.
.
.
...
...
. Find the solutions to
x
=
f
n
(
x
)
x = f_n(x)
x
=
f
n
(
x
)
for
n
>
0
n > 0
n
>
0
.
algebra
composition
Sequence