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Problem
Problem
If a polynomial function
f
f
f
satisfies the relation
log
2
(
f
(
x
)
)
=
log
2
(
2
+
2
3
+
2
9
+
…
)
⋅
log
3
\log_2(f(x)) = \log_2\left(2 + \frac{2}{3} + \frac{2}{9} + \dots\right) \cdot \log_3
lo
g
2
(
f
(
x
))
=
lo
g
2
(
2
+
3
2
+
9
2
+
…
)
⋅
lo
g
3
(
1
+
f
(
x
)
f
(
1
x
)
)
\left(1 + \frac{f(x)}{f\left(\frac{1}{x}\right)}\right)
(
1
+
f
(
x
1
)
f
(
x
)
)
and
f
(
10
)
=
1001
f(10) = 1001
f
(
10
)
=
1001
, then the value of
f
(
20
)
f(20)
f
(
20
)
is (a) 2002 (b) 7999 (c) 8001 (d) 16001
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