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.

$\begin{gathered} n+0.4x+5.7 \\ n-5.7=0.4x \\ x=\frac{n-5.7}{0.4} \\ =\frac{10n-57}{4} \end{gathered}$

So inverse of function is after interchange of variables,

$P^{-1}(x)=\frac{10x-57}{4}$

(c)

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

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

So answer is 6.5.