Question

the function P(m)below relates the amount of time (measured in minutes). Jane spent on her homework and the number of problems completed. it takes as input of the minutes worked and returns as output the number of problems completed. P(m)=m/5+8 which equation below represents the inverse function M(p), which takes the number of problems completed as input and returns the number of minutes worked? A. M(p)=40p+5 B. M(p)=40p-5 C. M(p)=5p+40 D. M(p)=5p-40

Answer 1

P(m)=m/5+8, the inverse function of P(m) is the function m(P):

P(m)=m/5+8 ===>=(m+40)/5====> ===>
Inverse of P(m) is m(P), plug the value of m into P ===>m(P) =5p-40

Answer 2

Follow these steps in finding the inverse of functions:

1. Replace function notation, is given, with y

2. Exchange independent variable and dependent variable (which is y here)

3. Solve for y

That new function is the inverse of the original.

Using the function
`P(m)=(m)/(5)+8`, we replace P(m) with y, to get:

`y=(m)/(5)+8`

Doing a little algebra and arranging:

`y=(m+40)/(5)`

Now we do step 2 and 3, we exchange y and m and then solve for y.

`m=(y+40)/(5)\\5m=y+40\\5m-40=y`

This is the inverse function.

Original function was P(m) so this function will be M(p). So we change m to p as the final touch.

M(p)=5p-40. Answer choice D is correct.

ANSWER: D