Question

The cost C of buying g gallons of gas at $2.39 per gallon is C = f(g) = $2.39g.

a) Inverse function: f^{-1}(x) = {x}/{2.39}
b) Independent variable: g, Dependent variable: C
c) f^{-1}(12) = 5.02, interpreted as Buying 12 gallons of gas costs $5.02.

Answer 1

The cost C of buying g gallons of gas at $2.39 per gallon is given by the equation C = f(g) = $2.39g. The inverse function of f(g) is f^-1(x) = x/2.39. The independent variable is g and the dependent variable is C.

Step-by-step explanation:

The cost C of buying g gallons of gas at $2.39 per gallon is given by the equation C = f(g) = $2.39g.

a) The inverse function of f(g) is f-1(x) = x/2.39. This means that if you know the cost of buying a certain amount of gas, you can find the number of gallons by dividing the cost by $2.39.

b) The independent variable in this equation is g, which represents the number of gallons. The dependent variable is C, which represents the cost.

c) To find f-1(12), substitute 12 for x in the inverse function f-1(x) = x/2.39. Therefore, f-1(12) = 12/2.39 = 5.02. This can be interpreted as buying 12 gallons of gas costs $5.02.