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