Question

3. Suppose the cost function for producing z pairs of a particular type of skates was given by C(z) 705.20+32.75 a) What is the inverse of this function? What does it represent? (Your answer should include complete sentences in contert.) b) Pick one ordered pair on the graph of the inverse function, and describe what it tells you about this situation. (Your answer should include complete sentences in contezt. c) Use the inverse to determine the number of pairs of skates that can be produced for an initial investment of $10,000. (Your answer should include complete sentences in contert)

Answer 1

C(x) 705.2 32.752.

to find the inverse function interchange the variables and solve for y

y = 705.2+32.752.

by interchange

r = 705.2 + 32.75

r-705.2 = 32.75

32.7-y = x-705.2

,_x- 705.2 32.75

....................(a)

2.-705.2 C-1 (r) = C-" - 705.2 32.75

it represent the number of pairs of a skates , when cost is x

.

.

to graph the function we need two points

x	2.-705.2 C-1 (r) = C-" - 705.2 32.75
705.2	705.2 -705.2 0 32.75 32.75
1500	1500-705.2794.8 24.26 32.75 32.75

draw a line between these two points

30 pairs of 20 skates (1032.7, 10) 500 1000 1500 cost

from the graph pick an ordered pair of (1032.7, 10)

here x axis represent cost and y-axis represent pairs of skates

which means , when cost is $1032.7 , then we can produce 10 pairs of skates

.

.

.

.

.

.

.now find number of pairs of skates when cost is 10000

.

$C^{-1}(10000) =\frac{10000-705.2}{32.75}$

9294.8 -1 (10000)-3275

for $10000, we can produce 283 pairs of skates