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Source:
January 1, 2022
algebra
Problem Statement
Let
f
(
x
)
=
x
+
a
x
+
b
f(x) =\frac{x+a}{x+b}
f
(
x
)
=
x
+
b
x
+
a
satisfy
f
(
f
(
f
(
x
)
)
)
=
x
f(f(f(x))) = x
f
(
f
(
f
(
x
)))
=
x
for real numbers
a
,
b
a, b
a
,
b
. If the maximum value of a is
p
/
q
p/q
p
/
q
, where
p
,
q
p, q
p
,
q
are relatively prime integers, what is
∣
p
∣
+
∣
q
∣
|p| + |q|
∣
p
∣
+
∣
q
∣
?
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