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3
2015 Algebra Tiebreaker #3
2015 Algebra Tiebreaker #3
Source:
July 1, 2022
2015
Algebra Tiebreaker
Problem Statement
Let
f
(
x
)
f(x)
f
(
x
)
be a polynomial of finite degree satisfying
(
x
+
9
)
f
(
x
+
1
)
=
(
x
+
3
)
f
(
x
+
3
)
(x+9)f(x+1)=(x+3)f(x+3)
(
x
+
9
)
f
(
x
+
1
)
=
(
x
+
3
)
f
(
x
+
3
)
for all real
x
x
x
. If
f
(
0
)
=
1
f(0)=1
f
(
0
)
=
1
, find the value of
f
(
1
)
f(1)
f
(
1
)
.
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