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VTRMC
1980 VTRMC
6
6
Part of
1980 VTRMC
Problems
(1)
1980 VTRMC #6
Source:
8/11/2020
Given the linear fractional transformation of
x
x
x
into
f
1
(
x
)
=
2
x
−
1
x
+
1
,
f_1(x) = \tfrac{2x-1}{x+1},
f
1
(
x
)
=
x
+
1
2
x
−
1
,
define
f
n
+
1
(
x
)
=
f
1
(
f
n
(
x
)
)
f_{n+1}(x) = f_1(f_n(x))
f
n
+
1
(
x
)
=
f
1
(
f
n
(
x
))
for
n
=
1
,
2
,
3
,
…
.
n=1,2,3,\ldots.
n
=
1
,
2
,
3
,
…
.
It can be shown that
f
35
=
f
5
.
f_{35} = f_5.
f
35
=
f
5
.
Determine
A
,
B
,
C
,
D
A,B,C,D
A
,
B
,
C
,
D
so that
f
28
(
x
)
=
A
x
+
B
C
x
+
D
.
f_{28}(x) = \tfrac{Ax+B}{Cx+D}.
f
28
(
x
)
=
C
x
+
D
A
x
+
B
.
linear algebra