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Please answer this question im in the middle of a quiz
The function below relates the amount of time (measured in minutes)
Steve spent on his homework and the number of problems completed.

It takes as input the number of minutes worked and returns as output the number of problems completed.

P(m)= (m/6)+9
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)=54p + 6

B. M(p)=54p - 6

C. M(p)=6p - 54

D. M(p)=6p + 54

Respuesta :

MrRoyal

Answer:

[tex]m(p) = 6p - 54[/tex]

Step-by-step explanation:

Given

[tex]P(m) = \frac{m}{6} + 9[/tex]

Required

Determine the inverse function

[tex]P(m) = \frac{m}{6} + 9[/tex]

Represent P(m) as P

[tex]P = \frac{m}{6} + 9[/tex]

Swap the positions of P and m

[tex]m = \frac{p}{6} + 9[/tex]

We are to make p the subject.

Subtract 9 from both sides

[tex]m -9= \frac{p}{6} + 9-9[/tex]

[tex]m -9= \frac{p}{6}[/tex]

Multiply through by 6

[tex]6(m -9)= \frac{p}{6} * 6[/tex]

[tex]6(m -9)= p[/tex]

[tex]6m -54= p[/tex]

Rearrange:

[tex]p = 6m -54[/tex]

Swap the positions of P and m

[tex]m = 6p - 54[/tex]

[tex]m(p) = 6p - 54[/tex]

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