Question

P (n), given below, is the price P in dollars for n grams of vitamins.P(n)=0.4n+5.7Complete the following statements.

Answer 1

(a)

In the function P(n) = 0.4n +5.7, P(n) is price of n grams of vitamins. So for the function x = P(n); x is price of n grams of vitamins.

The inverse of function determine amount of the vitamins for the known price of x dollars. So answer is,

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

(b)

Let P(n) = x, So

`x=0.4n+5.7`

Replace n by x and x by n in the given equation.

`n=0.4x+5.7`

Simplify the equation for x.

`\begin{gathered} n+0.4x+5.7 \\ n-5.7=0.4x \\ x=(n-5.7)/(0.4) \\ =(10n-57)/(4) \end{gathered}`

So inverse of function is after interchange of variables,

`P^(-1)(x)=(10x-57)/(4)`

(c)

Substitute 8.3 for x in the inverse equation to obtain the valur of P^-1(8.3).

`\begin{gathered} P^(-1)(8.3)=(10\cdot8.3-57)/(4) \\ =(83-57)/(4) \\ =(26)/(4) \\ =6.5 \end{gathered}`

So answer is 6.5.