MathDB
Problems
Contests
National and Regional Contests
China Contests
ASDAN Math Tournament
2015 ASDAN Math Tournament
8
2015 Team #8
2015 Team #8
Source:
August 3, 2022
2015
team test
Problem Statement
Let
f
(
x
)
=
x
+
a
x
+
b
f(x)=\tfrac{x+a}{x+b}
f
(
x
)
=
x
+
b
x
+
a
for real numbers
x
x
x
such that
x
≠
−
b
x\neq -b
x
=
−
b
. Compute all pairs of real numbers
(
a
,
b
)
(a,b)
(
a
,
b
)
such that
f
(
f
(
x
)
)
=
−
1
x
f(f(x))=-\tfrac{1}{x}
f
(
f
(
x
))
=
−
x
1
for
x
≠
0
x\neq0
x
=
0
.
Back to Problems
View on AoPS