Question

I’m not sure how to solve B and C

Answer 1

The function which represents the cost of producing x hearing aids is given by the following;

$f(x)=2840550+87x$

(A) The inverse of this function is determined as follows;

$\begin{gathered} f(x)=2840550+87x \\ y=2840550+87x \\ \text{Now interchange x variable for y variable;} \\ x=2840550+87y \\ Solve\text{ for y;} \\ x-2840550=87y \\ \text{Divide both sides by }87 \\ \frac{x-2840550}{87}=\frac{87y}{y} \\ y=\frac{x-2840550}{87} \\ \text{The inverse of the function therefore is;} \\ f(x)^{-1}=\frac{x-2840550}{87} \end{gathered}$

(B) From the inverse function we can determine the following;

INPUT = Cost of producing x units

OUTPUT = Number of units produced

(C) To determine the number of hearing aids that could be produced for a cost of 4,000,000;

$\begin{gathered} f(x)^{-1}=\frac{x-2840550}{87} \\ Where\text{ the cost is 4000000}; \\ f(4000000)=\frac{4000000-2840550}{87} \\ f(4000000)=\frac{1159450}{87} \\ f(4000000)=13327.0114\ldots \\ To\text{ the nearest whole number;} \\ f(4000000)=13,327 \end{gathered}$

At the cost of $4,000,000 the number of hearing aids that could be produced is 13,327.