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 \\ (x-2840550)/(87)=(87y)/(y) \\ y=(x-2840550)/(87) \\ \text{The inverse of the function therefore is;} \\ f(x)^(-1)=(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)=(x-2840550)/(87) \\ Where\text{ the cost is 4000000}; \\ f(4000000)=(4000000-2840550)/(87) \\ f(4000000)=(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.