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:

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

(a)

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

(b)

$P^{-1}(x)=\frac{x-5.3}{0.2}$

(c)

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