1 solve the equation by the using an inverse function (4x-5)^2=11, for xâ¥5/4
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2. Is f(x) = (x^4+x)/(x^3-6) a rational function
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Q18. 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 Q19. 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) Q20. Find functions f and g so that f â 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
Q29. 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) Q30. Solve the system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. a. x = 2, y = 3, z = -7; (2, 3, -7) b. x = 1, y = 3, z = -4; (1, 3, -4) c. x = 5, y = 13/2, z = -3; (5, 13/2, -3) d. x = 1, y = -3, z = -16; (1, -3, -16)
Q33. 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 Q34. Solve the linear programming problem. Minimize z = 11x + 6y + 7 subject to: x = 0, y = 0, x + y = 1. a. minimum: 7 b. minimum: 18 c. minimum: 24 d. minimum: 13 Q35. 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) Q36. Perform the row operations on the given augmented matrix. a. b. c. d. Q37. 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) Q38. 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) Q39. 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 Q40. Find the value of the determinant. a. 224 b. 24 c. -72 d. 72
