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MAA AMC
AMC 12/AHSME
1980 AMC 12/AHSME
14
Function of x
Function of x
Source:
December 31, 2005
function
quadratics
algebra
system of equations
Problem Statement
If the function
f
f
f
is defined by
f
(
x
)
=
c
x
2
x
+
3
,
x
≠
−
3
2
,
f(x)=\frac{cx}{2x+3} , ~~~x\neq -\frac 32 ,
f
(
x
)
=
2
x
+
3
c
x
,
x
=
−
2
3
,
satisfies
x
=
f
(
f
(
x
)
)
x=f(f(x))
x
=
f
(
f
(
x
))
for all real numbers
x
x
x
except
−
3
2
-\frac 32
−
2
3
, then
c
c
c
is
(A)
−
3
(B)
−
3
2
(C)
3
2
(D)
3
(E) not uniquely determined
\text{(A)} \ -3 \qquad \text{(B)} \ - \frac{3}{2} \qquad \text{(C)} \ \frac{3}{2} \qquad \text{(D)} \ 3 \qquad \text{(E)} \ \text{not uniquely determined}
(A)
−
3
(B)
−
2
3
(C)
2
3
(D)
3
(E)
not uniquely determined
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