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Mathematics
Mathematics
Problem
Let
f
1
(
x
)
=
3
x
+
2
2
x
+
3
f^1(x) = \frac{3x+2}{2x+3}
f
1
(
x
)
=
2
x
+
3
3
x
+
2
,
x
∈
R
−
{
−
3
2
}
x \in \mathbb{R} - \left\{-\frac{3}{2}\right\}
x
∈
R
−
{
−
2
3
}
. For
n
≥
2
n \ge 2
n
≥
2
, define
f
n
(
x
)
=
f
1
∘
f
n
−
1
(
x
)
f^n(x) = f^1 \circ f^{n-1}(x)
f
n
(
x
)
=
f
1
∘
f
n
−
1
(
x
)
. If
f
5
(
x
)
=
a
x
+
b
b
x
+
a
f^5(x) = \frac{ax+b}{bx+a}
f
5
(
x
)
=
b
x
+
a
a
x
+
b
,
gcd
(
a
,
b
)
=
1
\gcd(a, b) = 1
g
cd
(
a
,
b
)
=
1
, then
a
+
b
a + b
a
+
b
is equal to _____.
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