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Mathematics
Mathematics
Problem
Consider the function
p
(
x
)
=
{
x
2
−
4
,
1
≤
x
<
2
b
x
+
2
,
2
≤
x
≤
3
,
p(x)=\begin{cases}x^{2}-4,&1\le x<2\\bx+2,&2\le x\le 3\end{cases},
p
(
x
)
=
{
x
2
−
4
,
b
x
+
2
,
1
≤
x
<
2
2
≤
x
≤
3
,
where
b
b
b
is a real constant. For which value of
b
b
b
is the average value of
p
p
p
on
[
1
,
3
]
[1,3]
[
1
,
3
]
equal to
1
1
1
? a)
4
15
\dfrac{4}{15}
15
4
b)
16
15
\dfrac{16}{15}
15
16
c)
2
3
\dfrac{2}{3}
3
2
d)
1
1
1
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