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Problem Set A (1) For the function f(x)=1- 1x+2
find the following:
(i) f(-x)
(ii) f(x +k)
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- Concentration of a Mixture A 1000-liter tank contains 50 liters of a 25brine solution. You add xliters of a 75brine solution to the tank. (a) Show that the concentration C, the proportion of brine to total solution, in the final mixture is C=3x+504(x+50). (b) Determine the domain of the function based on the physical constraints of the problem. (c) Sketch the graph of the concentration function. (d) As the tank is filled, what happens to the rate at which the concentration of brine is increasing? What percent does the concentration of brine appear to approach?The profit function of Acrosonic company is given by P(x)=-0.02x^2+300x-200,000 dollars, where x is the number of Acrosonic model F loudspeaker systems produced. Find where the function P is increasing and decreasing. 1.) Increasing a.) The profit function P is increasing on(7500,∞) b.) The profit function P is increasing on(7500,0) c.) The profit function P is increasing on (0,7500) d.) The profit function P is increasing on(∞,7500) 2.) Decreasing a.) The profit function P is decreasing on(7500,∞) b.) The profit function P is decreasing on(7500,0) c.) The profit function P is deccreasing on (0,7500) d.) The profit function P is decreasing on(∞,7500)4. A manufacturer finds that the revenue generated by selling x units of a certain commodity is given by the function R(x)= 80x-0.4x^2, where the revenue R(x) is measured in dollars. What is the maximum revenue, and how many units should be manufactured to obtain this maximum? $....., at ....... units
- f(x)= -4x g(x)=3x-2 h(x)=x^2-6x. solve: f(x)+g(x)A power company burns coal to generate electricity, the cost c(x) to remove x% of the air pollutants is given by c(x)=600,000x/(100-x) determine if each statement is true, false, or cannot be determined a. The cost to remove 25% of the air pollutants is $400,000 b. If the company budgets $900,000 to remove pollutants, the can remove 100% of the pollutants c. The practical domain of the function is x union [0,100)f(x)= { x^2-1, x less than or equal to 32ax-4, x>3Find values of a for f (x) to be a continous function.
- x -3 -2 -1 0 1 2 3 f(x) 9 2 3 -4 -5 -8 -9 g(x) 3 0 6 2 -3 -1 -5 What is the value of f-1(g(-3)) a. -5 b. -3 c. -1 d. 1 e. cannot determine valuea. Domain b. Range c. f(-2) d. f(4) e. x-values where f(x)= -2 f. x-intercepts and y-interceptsA company's market research department recommends the manufacture and marketing of a new headphone. After suitable test marketing, the research department presents the following price-demand equation: x = 10000 - 1000 p. In the price-demand equation, the demand x is given as a function of price p. By solving for p, we obtain an equation in which the price p is given as a function of demand x: p = 10 - 0.001x where * is the number of headphones that retailers are likely to buy at Sp per set. The financial department provides the cost function C (x) = 7000 + 2x where $7000 is the estimate of fixed costs (tooling and overhead) and $2 is the estimate of variable costs per headphone (material, labor, marketing, transportation, storage, etc.). Find the domain of the function defined by the price-demand equation p. Find an interpret the marginal cost function. Find the revenue function as a function of and find its domain. Find the marginal revenue at x = 2000, 5000, 7000. Interpret these…
