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If a polynomial function satisfies _2(f(x))= _2 (2+ 23+ 29+ ) _3 (1+ f(x) f ( 1x ) ) and
MATHEMATICS · Single correct · AoPS · Mathematics · Functions · Functions
Problem
If a polynomial function
f
f
f
satisfies
log
2
(
f
(
x
)
)
=
log
2
(
2
+
2
3
+
2
9
+
⋯
)
log
3
(
1
+
f
(
x
)
f
(
1
x
)
)
\log_2(f(x))=\log_2\left(2+\frac23+\frac29+\cdots\right)\log_3\left(1+\frac{f(x)}{f\left(\frac1x\right)}\right)
lo
g
2
(
f
(
x
))
=
lo
g
2
(
2
+
3
2
+
9
2
+
⋯
)
lo
g
3
(
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
Related theory
Geometric Progressions
Functions
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