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QuestionJane did 8 homework problems. Find the inverse function m(p)m(p) from p(m)=m5+8p(m)=\frac{m}{5}+8. Which is correct? A. m(p)=5p−40m(p)=5 p-40 B. m(p)=40p+5m(p)=40 p+5 C. m(p)=5p+40m(p)=5 p+40 D. m(p)=40p−5m(p)=40 p-5

Studdy Solution

STEP 1

Assumptions1. The function p(m)p(m) is given by p(m)=m5+8p(m)=\frac{m}{5}+8. . The function p(m)p(m) relates the time (in minutes) Jane spent on her homework at home to the total number of problems she completed.
3. The input to the function p(m)p(m) is the number of minutes worked.
4. The output of the function p(m)p(m) is the number of problems completed.
5. We are asked to find the inverse function m(p)m(p), which uses problems completed as the input and gives minutes worked as the output.

STEP 2

To find the inverse of a function, we first replace the function notation p(m)p(m) with yy.
y=m5+8y = \frac{m}{5} +8

STEP 3

Next, we interchange the roles of yy and mm to find the inverse.
m=y5+8m = \frac{y}{5} +8

STEP 4

Now, we solve this equation for yy to find the inverse function m(p)m(p).
First, subtract8 from both sides of the equation.
m−8=ym -8 = \frac{y}{}

STEP 5

Then, multiply both sides of the equation by5 to isolate yy.
5(m−8)=y5(m -8) = y

STEP 6

Finally, replace yy with m(p)m(p) to get the inverse function.
m(p)=5(m−8)m(p) =5(m -8)

STEP 7

implify the equation to get the final form of the inverse function.
m(p)=5p−40m(p) =5p -40So, the correct answer is A. m(p)=5p−40m(p)=5 p-40.

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