Sure, let's work through the problem step-by-step.
1. Define the function [tex]\( p(x) \)[/tex]:
[tex]\[
p(x) = 2x - 1
\][/tex]
2. Calculate [tex]\( p(0) \)[/tex]:
[tex]\[
p(0) = 2(0) - 1 = -1
\][/tex]
3. Calculate [tex]\( p(8) \)[/tex]:
[tex]\[
p(8) = 2(8) - 1 = 16 - 1 = 15
\][/tex]
4. Calculate [tex]\( p(4) \)[/tex]:
[tex]\[
p(4) = 2(4) - 1 = 8 - 1 = 7
\][/tex]
5. Calculate [tex]\( M \)[/tex], which is given by:
[tex]\[
M = \frac{p(0) + p(8)}{p(4)}
\][/tex]
6. Substitute the values we found into the expression for [tex]\( M \)[/tex]:
[tex]\[
M = \frac{-1 + 15}{7}
\][/tex]
7. Simplify the numerator:
[tex]\[
-1 + 15 = 14
\][/tex]
8. Divide by the denominator:
[tex]\[
M = \frac{14}{7} = 2
\][/tex]
So, the detailed solutions for [tex]\( p(0) \)[/tex], [tex]\( p(8) \)[/tex], [tex]\( p(4) \)[/tex], and [tex]\( M \)[/tex] are:
[tex]\[
p(0) = -1, \quad p(8) = 15, \quad p(4) = 7, \quad \text{and} \quad M = 2.0
\][/tex]
