Question

Please help me with this problem

Answer 1

C
`P(v)=2(v+7)`

Explanation:

Lets say that
`P(v)=y` for simplicity.

In order to find the inverse of a function, we must switch the location of the variable, v, and y. Then we have to solve for y.

As we are already given the inverse, doing the same process again will give us the original function.

First we can set up the equation

`y=(1)/(2) v-7`

Next we can switch the location of the variables

`v=(1)/(2) y-7`

Now we can solve for y

`v=(1)/(2) y-7\\\\v+7=(1)/(2) y\\\\y=2(v+7)\\\\P(v)=2(v+7)`

This gives us the function

`P(v)=2(v+7)`

Answer 2

C P(v) = 2(v+7)

Explanation:

To find P(v), we need to take the inverse of P^-1 (v)

y = 1/2 v-7

Exchange y and v

v = 1/2 y-7

Solve for y

Add 7 to each side

v+7 = 1/2 y -7+7

v+7 = 1/2y

Multiply each side by 2

2(v+7) = 1/2 y*2

2(v+7) = y

P(v) = 2(v+7)