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Mathematics
Problem
The function
f
f
f
is defined by
f
(
t
)
=
t
f(t)=t
f
(
t
)
=
t
for
0
≤
t
≤
4
,
0\le t\le 4,
0
≤
t
≤
4
,
f
(
t
)
=
8
−
t
f(t)=8-t
f
(
t
)
=
8
−
t
for
4
<
t
≤
a
,
4<t\le a,
4
<
t
≤
a
,
where
a
>
4
a>4
a
>
4
. Let
g
(
x
)
=
∫
0
x
f
(
t
)
d
t
g(x)=\displaystyle\int_{0}^{x} f(t)\,dt
g
(
x
)
=
∫
0
x
f
(
t
)
d
t
. If
g
(
a
)
=
16
g(a)=16
g
(
a
)
=
16
, what is the value of
a
a
a
? a)
6
6
6
b)
11
11
11
c)
8
8
8
d)
12
12
12
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