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Mathematics
Mathematics
Problem
Let
a
a
a
be a real constant and define
f
(
x
)
=
(
x
−
a
)
(
x
+
2
)
(
x
−
a
)
(
x
−
1
)
f(x)=\frac{(x-a)(x+2)}{(x-a)(x-1)}
f
(
x
)
=
(
x
−
a
)
(
x
−
1
)
(
x
−
a
)
(
x
+
2
)
for all
x
x
x
in its domain. For exactly one of the following values of
a
a
a
, the range of
f
f
f
excludes the value
5
2
\dfrac{5}{2}
2
5
. Which value of
a
a
a
is it? a)
a
=
5
3
\displaystyle a=\frac{5}{3}
a
=
3
5
b)
a
=
5
2
\displaystyle a=\frac{5}{2}
a
=
2
5
c)
a
=
3
\displaystyle a=3
a
=
3
d)
a
=
1
\displaystyle a=1
a
=
1
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