Question

Finding, evaluating, and Interbreeding an inverse function forgiven linear relationship

Answer 1

Let:

`\begin{gathered} P(n)=y \\ y=0.2n+5.3 \end{gathered}`
`n=0.2y+5.3`

Solve for y:

`\begin{gathered} y=(n-5.3)/(0.2) \\ so\colon \\ P^(-1)(n)=(n-5.3)/(0.2) \end{gathered}`

(a)

The amount of vitamins (in grams) for a price of x dollars

(b)

`P^(-1)(x)=(x-5.3)/(0.2)`

(c)

`\begin{gathered} P^(-1)(6.6)=(6.6-5.3)/(0.2) \\ P^(-1)(6.6)=(1.3)/(0.2) \\ P^(-1)(6.6)=6.5 \end{gathered}`