To find the inverse function \( m(p) \) from the given function \( p(m) = \frac{m}{4} + 7 \), follow these steps:
1. Start with the given function:
[tex]\[
p(m) = \frac{m}{4} + 7
\][/tex]
2. Rewrite the equation to express \( m \) in terms of \( p \). Begin by isolating \( \frac{m}{4} \) on one side of the equation:
[tex]\[
p = \frac{m}{4} + 7
\][/tex]
3. Subtract 7 from both sides of the equation to move the constant term:
[tex]\[
p - 7 = \frac{m}{4}
\][/tex]
4. To clear the fraction, multiply both sides by 4:
[tex]\[
4(p - 7) = m
\][/tex]
5. Simplify the expression:
[tex]\[
m = 4(p - 7) = 4p - 28
\][/tex]
Therefore, the inverse function, which represents the minutes worked \( m \) as a function of the problems completed \( p \), is:
[tex]\[
m(p) = 4p - 28
\][/tex]
Correspondingly, the correct answer is:
D. [tex]\( m(p) = 4p - 28 \)[/tex]
