264 CHAPTER 4 Polynomial and Rational Functions In Problems 9–14, solve the inequality by using the graph of the function. [Hint: The graphs were drawn in Problems 5–10 of Section 4.2.] 9. Solve ( ) < f x 0, where ( ) ( ) = − f x x x 3 2 . 10. Solve ( ) ≤ f x 0, where ( ) ( ) = + f x x x 2 2. 11. Solve ( ) ≥ f x 0, where ( ) ( ) ( ) = + − f x x x 4 1 2 . 12. Solve ( ) > f x 0, where ( ) ( )( ) = − + f x x x 1 3 2. 13. Solve ( ) ≤ f x 0, where ( ) ( )( ) = − + − f x x x 2 2 2 3. 14. Solve ( ) < f x 0, where ( ) ( )( ) = − + − f x x x 1 2 4 1 3. In Problems 15–18, solve the inequality by using the graph of the function. [Hint: The graphs were drawn in Problems 7–10 of Section 4.6.] 15. Solve ( ) > R x 0, where ( ) ( ) = + + R x x x x 1 4 . 16. Solve ( ) < R x 0, where ( ) ( )( ) = − + R x x x x 1 2 . 17. Solve ( ) ≤ R x 0, where ( ) = + + R x x x 3 3 2 4 . 18. Solve ( ) ≥ R x 0, where ( ) = + − R x x x 2 4 1 . In Problems 19–54, solve each inequality algebraically. 19. ( ) ( ) − + < x x 4 6 0 2 20. ( )( ) − + > x x 5 2 0 2 21. − > x x4 0 3 2 22. + < x x8 0 3 2 23. >− x x 2 8 3 2 24. <− x x 3 15 3 2 25. ( )( )( ) + − − ≤ x x x 2 4 6 0 26. ( )( )( ) + + + ≤ x x x 1 2 3 0 27. − − > x x x 4 12 0 3 2 28. + − > x x x 2 3 0 3 2 29. > x x 4 2 30. < x x9 4 2 31. > x 1 4 32. > x 1 3 33. ( ) ( ) − < − + x x x 3 2 2 1 2 2 2 34. ( )( ) − + < + + x x x x 3 2 3 5 2 35. + − > x x 1 1 0 36. − + > x x 3 1 0 37. ( )( ) − + ≤ x x x 2 2 0 38. ( )( ) − + − ≤ x x x 3 2 1 0 39. ( ) − − ≥ x x 3 4 0 2 2 40. ( ) + − ≥ x x 5 4 0 2 2 41. + − ≤ x x 4 2 1 42. + − ≥ x x 2 4 1 43. − + ≤ x x 3 5 2 2 44. − + ≥ x x 4 2 4 1 45. + − ≤ x x 1 3 2 46. − + ≥− x x 1 2 2 47. − < − x x 1 2 2 3 9 48. − > + x x 5 3 3 1 49. ( )( ) ( )( ) + + + − ≥ x x x x x 3 4 5 1 0 2 50. ( )( ) ( )( ) + − − + ≥ x x x x x 1 2 1 1 0 2 51. ( ) ( ) − + − < x x x 3 2 1 1 0 3 3 52. ( ) ( ) − − + < x x x 2 3 2 1 0 3 3 53. − < x x 6 5 6 54. + < x x 12 7 Mixed Practice In Problems 55–58, (a) graph each function by hand, and (b) solve ( ) ≥ f x 0. 55. ( ) = + − − + f x x x x x 5 6 4 4 2 2 56. ( ) = + + − f x x x x 2 9 9 4 2 2 57. ( ) ( ) ( ) = + − − − − f x x x x x x 4 2 3 6 2 2 58. ( ) ( ) ( ) = − − + + − f x x x x x x 1 5 4 20 2 2 59. For what positive numbers is the cube of the number greater than four times its square? 60. For what positive numbers is the cube of the number less than the number? 61. What is the domain of the function ( ) = − f x x 16? 4 62. What is the domain of the function ( ) = − f x x x3 ? 3 2 63. What is the domain of the function ( ) = − + f x x x 2 4 ? 64. What is the domain of the function ( ) = − + f x x x 1 4 ? In Problems 65–68, determine where the graph of f is below the graph of g by solving the inequality ( ) ( ) ≤ f x g x .Graphf and g together. 65. ( ) ( ) = − = − + f x x g x x 1 2 2 4 2 66. ( ) ( ) = − = − f x x g x x 1 1 4 67. ( ) ( ) = − = f x x g x x 4 3 4 2 68. ( ) ( ) = = − f x x g x x 2 4 2 69. Where is the graph of ( ) = − − R x x x 16 9 4 2 above the x-axis? 70. Where is the graph of ( ) = − − R x x x 8 25 3 2 above the x-axis? Applications and Extensions
RkJQdWJsaXNoZXIy NjM5ODQ=