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Contests
National and Regional Contests
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MAA AMC
AMC 10
2000 AMC 10
24
Function
Function
Source:
February 24, 2006
function
Vieta
algebra
polynomial
AMC
Problem Statement
Let
f
f
f
be a function for which
f
(
x
3
)
=
x
2
+
x
+
1
f\left(\frac x3\right)=x^2+x+1
f
(
3
x
)
=
x
2
+
x
+
1
. Find the sum of all values of
z
z
z
for which
f
(
3
z
)
=
7
f(3z)=7
f
(
3
z
)
=
7
.
(A)
−
1
3
(B)
−
1
9
(C)
0
(D)
5
9
(E)
5
3
\text{(A)}\ -\frac13\qquad\text{(B)}\ -\frac19 \qquad\text{(C)}\ 0 \qquad\text{(D)}\ \frac59 \qquad\text{(E)}\ \frac53
(A)
−
3
1
(B)
−
9
1
(C)
0
(D)
9
5
(E)
3
5
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