The demand function for an auto parts manufacturing company is given by f(x)= 100,000-2,500, where x represents price and f(x) represents quantity.
f^1 (x) = in the inverse function, the variable x represents
40-2500/x price
40+x/2500 quantity
40-x/2500
40+2500/x

Answer

Part 1) f(x)⁻¹ = 40 - x/2,500

Part 2) quantity

Explanation

f(x)= 100,000-2,500x

In finding the inverse of F(x) we make x the suject of the formula.

f(x)= 100,000-2,500x

2,500x = 100,000 - f(x)

x = 100,000/2,500 - f(x)/2500

x = 40 - f(x)/2,500

Now interchange x with f(x).

f(x)⁻¹ = 40 - x/2,500

d. bc = 12 and ef = 16

step-by-step explanation:

we are given that δabc : δdef such that .

also, it is given that

so, from the options, we need that .

a.

b.

c.  

d.

as, we can see that only option d gives the same ratio as i.e. .

hence, the possible lengths are bc = 12 and ef = 16.

answer: the price of one pound cabbage = $ 0.8

the point (10,8) represents that the cost of 10 pounds cabbage is $ 8

step-by-step explanation:

since, here is a proportional relation between the number of pounds of cabbage (x) and the price in dollars (y).

therefore, we can write,

⇒ y = k x

where k is the constant of proportionality.

now, point (5,4) is in the line.

thus, it will satisfies the above equation of line.

⇒ 4 = 5 k

⇒ k = 0.8

thus, the equation of the line is,

y = 0.8 x

a) for x = 1,

y = 0.8

therefore, the cost of one pound of cabbage is 0.8 dollars.

b) in the below graph (10,8) represents that the cost of 10 pounds of cabbage is 8 dollars.