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Sweden Contests
Swedish Mathematical Competition
1993 Swedish Mathematical Competition
6
6
Part of
1993 Swedish Mathematical Competition
Problems
(1)
f(x_1) = x_2, f(x_2) = x_3 , f(x_3) = x_1 if f(x) = 1/(ax+b)
Source: 1993 Swedish Mathematical Competition p6
4/2/2021
For real numbers
a
a
a
and
b
b
b
define
f
(
x
)
=
1
a
x
+
b
f(x) = \frac{1}{ax+b}
f
(
x
)
=
a
x
+
b
1
. For which
a
a
a
and
b
b
b
are there three distinct real numbers
x
1
,
x
2
,
x
3
x_1,x_2,x_3
x
1
,
x
2
,
x
3
such that
f
(
x
1
)
=
x
2
f(x_1) = x_2
f
(
x
1
)
=
x
2
,
f
(
x
2
)
=
x
3
f(x_2) = x_3
f
(
x
2
)
=
x
3
and
f
(
x
3
)
=
x
1
f(x_3) = x_1
f
(
x
3
)
=
x
1
?
function
algebra