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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.

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