# Precalculus

posted by .

Suppose daily operating profit, in dollars, for a movie theater is a function of the number of tickets sold with the rule P(x)=8.5x-2,500, for 0≤x≤1,000.

a) Explain why the profit function has an inverse
b) P(400)=900. Rewrite this equation in terms of P^-1.
c) Verify that P^-1(4470)=820 and describe what this equation means in this context.
d) Find a rule for P^-1(x) and then verify the P^-1(P(450))=450

• Precalculus -

is x the tickets sold? Assuming yes...

a. given a profit, there is only one number of tickets that could have been sold.

b. P^-1(900)=400

c. it means that 4470 of revenue translates to 820 tickets.
P(820)=8.5(820)-2500=4470 check that.

d. I don't understand what the question wants.

## Similar Questions

1. ### algebra

Annual profit in thousands of dollars is given by the function,p(x)=200square x-3 +10,000,where x is the number of items sold in thousands, x less than 3. describe the meaning of the numbers 3 and 10,000 in the formula. find the profit …
2. ### math

A movie theater seats 500 people. For any particular show, the amount of money the theater makes is a function m(n) of the number of people, n, in attendance. If a ticket costs 2 dollars, find the domain and range of this function. …
3. ### Math

Gymnast Clothing manufactures expensive soccer cleats for sale to college bookstores in runs of up to 500. Its cost (in dollars) for a run of x pairs of cleats is C(x) = 3000 + 9x + 0.1x2 (0 ≤ x ≤ 500). Gymnast Clothing …
4. ### Algebra

Gymnast Clothing manufactures expensive soccer cleats for sale to college bookstores in runs of up to 500. Its cost (in dollars) for a run of x pairs of cleats is C(x) = 3000 + 9x + 0.1x2 (0 ≤ x ≤ 500). Gymnast Clothing …
5. ### Algebra

Gymnast Clothing manufactures expensive soccer cleats for sale to college bookstores in runs of up to 500. Its cost (in dollars) for a run of x pairs of cleats is C(x) = 3000 + 9x + 0.1x2 (0 ≤ x ≤ 500). Gymnast Clothing …
6. ### Math

A factory produces x calculators per day. The total daily cost in Shillings incured is 5x^2-800x+500. If the calculators are sold for sh (100-10x) each, i, Determine the profit function ii, Find the number of calculators that would …
7. ### Math

A factory produces x calculators per day. The total daily cost in Shillings incured is 5x^2-800x+500. If the calculators are sold for sh (100-10x) each, i, Determine the profit function ii, Find the number of calculators that would …
8. ### Math

A factory produces x calculators per day. The total daily cost in Shillings incured is 5x^2-800x+500. If the calculators are sold for sh (100-10x) each, i, Determine the profit function ii, Find the number of calculators that would …
9. ### math

A profit function is derived from the production cost and revenue function for a given item. The monthly profit function for a certain item is given by P(x)=−0.05x^2+400x−100,000, where P is in dollars and x is the number …
10. ### math

A profit function is derived from the production cost and revenue function for a given item. The monthly profit function for a certain item is given by P(x)=−0.05x2+500x−100,000, where P is in dollars and x is the number …

More Similar Questions