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Unformatted text preview: Name Date Math 10250 Review for Exam 1 1. (a) Determine the natural domain of f ( x ) = 2 x x 1 , find also its inverse g ( x ). Ans. x 6 = 1; g ( x ) = x +2 x +1 (b) What is the natural domain of f ( x ) = √ 3 2 x ? Ans. x ≤ 3 / 2 2. A brand of sunglasses selling for $50 each has a demand of 1,500 units. However, when the price is increased by $5, its demand is decreased by 100 units. Find its demand assuming that is a linear function. Ans. q = D ( p ) = 20 p + 2 , 500 3. Complete the square for each quadratic and then sketch its graph. (i) f ( x ) = 3 x 2 + 12 x (ii) f ( x ) = 2 x 2 12 x + 10. y x 2 1 Ans. (i) f ( x ) = 3( x 2) 2 + 12; (ii) f ( x ) = 2( x 3) 2 8 4. When the price p of a particular computer is $2,000 then the demand x is 50,000 units per week. However, when the price drops by $500 then the demand rises by 25,000 units. On the cost side, the company making these computers has $40,000,000 fixed cost and $600 expenses per unit. Assuming that the demand is linear , find the profit function P in terms of x and its maximum value....
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This note was uploaded on 03/02/2012 for the course MATH 10250 taught by Professor Himonas during the Fall '08 term at Notre Dame.
 Fall '08
 HIMONAS
 Math, Calculus

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