Alex completed 7 homework problems in class. The function p(m) relates thetime (in minutes) Alex spent on his homework at home to the total number ofproblems he completed. The input is the number of minutes worked. Theoutput is the number of problems completed.p(m)=m/4+7Which equation represents the inverse function m(p), which uses problemscompleted as the input and gives minutes worked as the output?

Accepted Solution

Hello!The answer is:D. [tex]m(p)=4p-28[/tex]Why?Inversing a function consists of switching the function (name) and the variable, so, where we have the variable (m for this case) we should rewrite it as the function (p(m)), and then, isolate the function in order to know the inverse function.So, we are given the function:[tex]p(m)=\frac{m}{4}+7[/tex]We know that:[tex]p(m)^{-1}=m(p)[/tex]Then, rewriting and calculating, we have:[tex]p(m)=\frac{m}{4}+7[/tex][tex]p=\frac{m(p)}{4}+7\\\\p-7=\frac{m(p)}{4}\\\\m(p)=(p-7)*4=4p-28[/tex]Hence, we have that the answer is:D. [tex]m(p)=4p-28[/tex]Have a nice day!