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Unformatted text preview: CORRECTION AND COMMENTS Quizz 1, Sept 4 Math 118: 39439 Fall 2008
Name (in capitals): Present answers clearly and with reasonable detail in this page. If needed, use the back of this sheet for scratch. You have 25 minutes for this 5 points quiz. Good work. Consider the functions f (x) = and g(x) = x + 1. PROBLEM x2 x1 (a) (1 pts) Indicate the domain of f (x). Since x  1 is not allowed to be zero, the domain of f (x) is all real numbers except number 1. 1 (b) (1 pts) Find the composition f (g(x)).
f (g(x)) = f (x + 1) = (x + 1)  2 x + (1  2) x1 = = . (x + 1)  1 x + (1  1) x PROBLEM Consider a supply price function given by S(x) = x2  3x  10, also, consider a demand price function given by D(x) = 6  3x, where x stands for the number of units of a certain commodity. (a) (2 pts) Name pe the equilibrium price and xe the equilibrium number of units. Find xe and pe . Equilibrium price occurs when demand equals supply. Search for x s.t.:
S(x) = D(x) x2  3x  10 = 6  3x x2  3x  10  6 + 3x = 0 x2  16 = 0 (x  4)(x + 4) = 0 1 Comments:
etc. with symbols this can be written as x = 1,R\{1}, (, 1)(1, +), {x R; x = 1}, i x = 4 or x = 4. Since x refers to number of units it should be positive. Therefore xe = 4. To nd pe , plug in the xe in demand or supply. D(4) = 6  (3)(4) = 6. Since we shouldn't allow negative prices either, this problem has no solution. Mathematically, by solving D(x) = S(x) we will obtain two solutions xe = 4 and pe = 6 or xe = 4 and pe = 18, which correspond to the two points of intersection of the graphs of the functions S(x) and D(x). (b) (1 pts) Sketch of the graph of D(x) indicating its xintercept and y intercept. The y intercept is (0, 6) because D(0) = 6  (3)(0) = 6; the xintercept is (2, 0) because 0 = 6  3x i x = 2. The graph is a line through those points.
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 Fall '07
 Vorel
 Math, Calculus

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