# Dan works at a hardware store. The employee discount is determined by the

formula d = 0.15 (c − 10 ). Use the inverse of this function to find the cost of the item for which Dan received an $18.00 discount.

a. Find the inverse function that models cost as a function of the discount.

b. Evaluate the inverse function for d = 18.

c. What was Dan’s final cost for this item?

## a. The inverse function that models cost as a function of the discount is found by solving for c in terms of d. So, let's do some math magic:

d = 0.15(c - 10)

Solving for c:

c - 10 = d / 0.15

c = (d / 0.15) + 10

Therefore, the inverse function is c = (d / 0.15) + 10.

b. To evaluate the inverse function for d = 18, simply plug in d = 18:

c = (18 / 0.15) + 10

c = 120 + 10

c = 130

So, the cost of the item for which Dan received an $18.00 discount is $130.

c. Dan's final cost for this item is $130.

## a. To find the inverse function that models cost as a function of the discount, we need to switch the roles of the variables "c" and "d" in the original formula.

Let's denote the inverse function as "f", so we have:

c = f(d)

Now we can rearrange the original formula to solve for "c":

d = 0.15(c - 10)

d/0.15 = c - 10

d/0.15 + 10 = c

Therefore, the inverse function that models cost as a function of the discount is:

f(d) = d/0.15 + 10

b. To evaluate the inverse function for d = 18, we substitute the value of "d" into the inverse function:

f(18) = 18/0.15 + 10

f(18) = 120 + 10

f(18) = 130

So, when Dan received an $18 discount, the cost of the item was $130.

c. Dan's final cost for this item was $130.

## To find the inverse function that models cost as a function of the discount, we need to solve for c in terms of d.

The formula for the employee discount is given as:

d = 0.15(c - 10)

To find the inverse function, we need to swap the roles of d and c and solve for c.

So, let's rearrange the formula:

d = 0.15(c - 10)

d/0.15 = c - 10

c = d/0.15 + 10

Therefore, the inverse function that models cost as a function of the discount is:

c = d/0.15 + 10

To evaluate the inverse function for d = 18, we substitute d = 18 into the equation c = d/0.15 + 10:

c = (18/0.15) + 10

c ≈ 120 + 10

c ≈ 130

So, the cost of the item for which Dan received an $18.00 discount is approximately $130.

Therefore, Dan's final cost for this item was $130.

## I don't think you are using the concept of the "inverse of a function" in the proper way, you are just solving the equation for c

d = .15c - 1.5

.15c = d + 1.5

c = (d+1.5)/.15

now plug in d = 18

c = (18+1.5)/.15 = 130

We could have just plugged in d = 18 in the original

18 =.15(c-10)

18/.15 = c-10

120 = c - 10

130 = c