For this case, we have a function of the form:
[tex]y = P (m)[/tex]
Where "y" represents the number of problems completed.
We must find the inverse function of:
[tex]P (m) = \frac {m} {4} +7[/tex]
For this, we perform the following steps:
We change P(m) to y:
[tex]y = \frac {m} {4} +7[/tex]
We clear the variable "m":
[tex]y-7 = \frac {m} {4}[/tex]
[tex]4 (y-7) = m[/tex]
We change m to[tex]f ^ {-1} (m)[/tex]:
[tex]4 (y-7) = f ^ {- 1} (m)\\f ^ {- 1} (m) = 4y-28[/tex]
Taking into account that "y" represents the number of problems completed, we substitute "y" for "p":
[tex]f ^ {- 1} (m) = 4p-28\\M (p) = 4p-28[/tex]
Answer:
Option D
