1. Find functions f and g so that f g = H(x) = (5 - 2x3)2. a. f(x) = 5 - 2x3 ; g(x) = x2 b. f(x) = (5 - 2x)3 ; g(x) = x2 c. f(x) = x2 ; g(x) = 5 - 2x3 d. f(x) = x3 ; g(x) = (5 - 2x)2 Q2. Find the inverse of the function and state its domain and range. {(-3, 4), (-1, 5), (0, 2), (2, 6), (5, 7)} a. {(3, 4), (1, 5), (0, 2), (-2, 6), (-5, 7)}; D = {3, 1, 0, -2, -5}; R = {2, 4, 5, 6, 7} b. {(-3, -4), (-1, -5), (0, -2), (2, -6), (5, -7)}; D = {-3, -1, 0, 2, 5}; R = {-7, -6, -5, -4, -2} c. {(4, -3), (5, -1), (2, 0), (6, 2), (7, 5)} D = {2, 4, 5, 6, 7}; R = {-3, -1, 0, 2, 5} d. {(3, -4), (1, -5), (0, -2), (-2, -6), (-5, -7)}; D = {3, 1, 0, -2, -5}; R = {-7, -6, -5, -4, -2} Q3. Solve the equation log 4 (x + 2) = -1 a. {-7} b. {-7/4} c. {9/4} d. {9} Q4. If f(x) = 4x and g(x) = 12, find the point of intersection of the graphs of f and g by solving f(x) = g(x). Give an exact answer. a. (log 4 12, 12) b. (log 4 12, 4) c. (log 4 12, 0) d. (12, 12) Q5. Write log 2 (7m 3n)/k2 as the sum and/or difference of logarithms. Express powers as factors. a. (1/7) log 2 m + (1/3) log 2 n - 2log 2 k b. (1/7) log 2 m (1/3) log 2 n 2log 2 k c. 7log 2 m + 3log 2 n - 2log 2 k d. (7/2) log 2 m + (3/2) log 2 n - (2/2) log 2 k Q6. Change the exponential expression 5-3 = 1/125 to an equivalent expression involving a logarithm. a. log -3 1/125 = 5 b. log 5 1/125 = -3 c. log 5 -3 = 1/125 d. log 1/125 5 = -3 Q7. Write log 7 (xy)/15 as the sum and/or difference of logarithms. Express powers as factors. a. (1/2) log 7 xy - (1/2) log 7 15 b. (1/2) log 7 x (1/2) log 7 y (1/2) log 7 15 c. (1/2) log 7 x + (1/2) log 7 y - (1/2) log 7 15 d. (1/2) log 7 x + (1/2) log 7 y - log 7 15 Q8. Solve the equation 3x = 81. a. {27} b. {5} c. {4} d. {3} Q9. A size 6 dress in Country C is size 52 in Country D. A function that converts dress sizes in Country C to those in Country D is f(x) = 2(x + 20). Find a formula for the inverse of the function described. a. f -1(x) = (x - 20)/2 b. f -1(x) = x - 20 c. f -1(x) = (x/2) - 20 d. f -1(x) = (x/2) + 20 Q10. Solve the equation 3(1 + 2x) = 243. a. {81} b. {2} c. {-2} d. {6} Q11. Find the domain of the composite function f g if f(x) = 28/x and g(x) = -8/(x - 7). a. {x | x 7} b. {x | x 0, x 7, x 4} c. {x | x 7, x 0} d. {x | x is any real number} Q12. The graph of a one-to-one function f(x) = x + 2 is given. Draw the graph of the inverse function f-1 as a dashed line or curve. a. b. Q13. Find the present value to get $6500 after 2 years at 5% compounded quarterly. Round to the nearest cent. a. $5895.69 b. $614.91 c. $5885.09 d. $5958.65 Q14. Find the domain of the function f(x) = log 5 (100 - x2). a. (-10, 10) b. (-, -10) (10, ) c. (-100, 100) d. [-10, 10] Q15. For the functions f(x) = x2 + 4 and g(x) = x2 + 1, find the composite function (f g)(x). a. x4 + 5 b. x4 + 17 c. x4 + 2x2 + 5 d. x4 + 8x2 + 17 Q16. Use the horizontal line test to determine whether the function is one-to-one. a. Yes b. No Q17. Solve the equation log 72 (x2 - x) = 1. a. {-8, -9} b. {1, 72} c. {8, 9} d. {-8, 9} Q18. The value of a particular investment follows a pattern of exponential growth. You invested money in a money market account. The value of your investment t years after your initial investment is given by the exponential growth model A = 5100e0.047t. How much did you initially invest in the account? a. $2550.00 b. $5345.42 c. $5100.00 d. $239.70 Q19. Find the exact value of the logarithmic expression log 4 1/64. a. -1/3 b. -3 c. 1/3 d. 3 Q20. Find the amount that results from the investment of $12,000 invested at 5% compounded quarterly after a period of 8 years. a. $5857.57 b. $17,729.47 c. $17,857.57 d. $17,637.10 Q21. Graph the inequality x + y < -5. a. b. c. d. Q22. Solve the system of equations using substitution. a. x = -6, y = 7; x = -7, y = 6 or (-6, 7), (-7, 6) b. x = -6, y = -7; x = -7, y = -6 or (-6, -7), (-7, -6) c. x = 6, y = -7; x = 7, y = -6 or (6, -7), (7, -6) d. x = 6, y = 7; x = 7, y = 6 or (6, 7), (7, 6) Q23. Write the augmented matrix for the system. a. b. c. d. Q24. Find the value of the determinant. a. 224 b. 24 c. -72 d. 72 Q25. Solve the system of equations using Cramer's Rule if it is applicable. a. x = -4, y = 3; (-4, 3) b. x = -3, y = -4; (-3, -4) c. x = 4, y = 3; (4, 3) d. x = 3, y = 4; (3, 4) Q26. a. b. c. d. Q27. Solve the system of equations using Cramer's Rule if it is applicable. a. x = 9, y = 2, z = 5; (9, 2, 5) b. x = 8, y = 4, z = 5; (8, 4, 5) c. x = 4, y = 5, z = 4; (4, 5, 4) d. x = 8, y = -4, z = -5; (8, -4, -5) Q28. A dietitian needs to purchase food for patients. She can purchase an ounce of chicken for $0.25 and an ounce of potatoes for $0.03. Let x = the number of ounces of chicken and y = the number of ounces of potatoes purchased per patient. Write the objective function that describes the total cost per patient per meal. a. z = 3y + 25y b. z = 0.25x + 0.03y c. z = 25x + 3y d. z = 0.03x + 0.25y Q29. Perform the row operations on the given augmented matrix. a. b. c. d. Q30. Solve the system of equations using substitution. a. x = 2, y = 4; x = 2, y = -4; x = -2, y = 0 or (2, 4), (2, -4), (-2, 0) b. x = 2, y = 4; x = -2, y = 0 or (2, 4), (-2, 0) c. x = 2, y = 4; x = 2, y = -4 or (2, 4), (2, -4) d. x = 2, y = 4 or (2, 4) Q31. Solve the system of equations. a. x = -4, y = 4, z = -3; (-4, 4, -3) b. x = -3, y = 4, z = -4; (-3, 4, -4) c. x = -4, y = -3, z = 4; (-4, -3, 4) d. inconsistent Q32. Write the partial fraction decomposition of the rational expression (4x3 + 4x2)/(x2 + 5)2. a. (4x - 4)/(x2 + 5) + (-20x + 20)/(x2 + 5)2 b. (4x + 4)/(x2 + 5) + (-20x - 20)/(x2 + 5)2 c. (4x + 4)/(x2 + 5) + (20x - 20)/(x2 + 5)2 d. (4x + 4)/(x2 + 5) + (20x + 20)/(x2 + 5)2 Q33. Solve the system of equations by substitution. a. x = 2, y = 9; (2, 9) b. x = 3, y = 9; (3, 9) c. x = 3, y = 8; (3, 8) d. x = 2, y = 8; (2, 8) Q34. A flat rectangular piece of aluminum has a perimeter of 58 inches. The length is 7 inches longer than the width. Find the width. a. 18 in. b. 29 in. c. 11 in. d. 25 in. Q35. Write the partial fraction decomposition of the rational expression x/(x2 - 9x + 20). a. -4/(x - 4) + 5/(x - 5) b. -5/(x - 4) + 4/(x - 5) c. 4/(x - 4) + -5/(x - 5) d. -4/(x - 4) + -5/(x - 5) Q36. Write the partial fraction decomposition of the rational expression (14x + 1)/[(x - 1)(x2 + x + 1)]. a. 5/(x - 1) + (4x - 5)/(x2 + x + 1) b. 5/(x - 1) + (-5x + 4)/(x2 + x + 1) c. 5/(x - 1) + -5/(x + 1) + 4/(x - 1) d. -5/(x - 1) + (5x + 4)/(x2 + x + 1) Q37. Solve the system of equations by elimination. a. x = 10, y = 0; (10, 0) b. x = 10, y = 10; (10, 10) c. x = 0, y = 10; (0, 10) d. x = 0, y = 0; (0, 0) Q38. a. b. c. d. Q39. Find the inverse of the matrix. Be sure to check your answer. a. b. c. d. Q40. Graph the solution set of the system of inequalities or indicate that the system has no solution. a. b. c. d