Let C=f(q)=450+0.2q give the cost in dollars to manufacture q kg of a chemical.

a) Which of the following statement(s) correctly explain the meaning of f^(−1)(C)
b)Find a formula for f^(−1)(C)=

the inverse will be kg of q/dollarcost

1/f(q)=1/(450+.2q)

no, that is the reciprocal. The inverse function is

f^-1(C) = (C-450)/.2 = 5C - 2250

That is the number of kg of q it takes to cost C dollars.

a) To understand the meaning of f^(-1)(C), we need to recognize that f(q) represents the cost in dollars to manufacture q kg of a chemical.

The function f^(-1)(C), on the other hand, represents the inverse function of f(q). In other words, it gives us the value of q (the amount of chemical in kg) that corresponds to a given cost C in dollars.

So, with that in mind, let's examine the following statements:

1) f^(-1)(C) represents the cost in dollars for a given value of q.
This statement is incorrect because f^(-1)(C) does not represent the cost in dollars. It represents the quantity of chemical in kg (q) for a given cost C.

2) f^(-1)(C) represents the amount of chemical in kg for a given cost in dollars.
This statement is correct because it accurately describes the meaning of f^(-1)(C). It represents the amount of chemical in kg (q) for a given cost C in dollars.

b) To find the formula for f^(-1)(C), we need to solve the equation C = f(q) for q.

Given that C = 450 + 0.2q, we can start by subtracting 450 from both sides to isolate the 0.2q term:

C - 450 = 0.2q

Next, we divide both sides of the equation by 0.2 to solve for q:

(q) = (C - 450)/0.2

Simplifying further, we have:

q = (C - 450)/0.2

Therefore, the formula for f^(-1)(C) is q = (C - 450)/0.2. This formula allows us to calculate the quantity of chemical in kg for a given cost in dollars.