chapter 0

chapter 0 - Chapter 0 Exercises 0.1 1 2 3 4 5 6 7[2 3 3 8 1...

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Chapter 0 Exercises 0.1 1. 0 –1 4 2. 03 π 4 3. 0 –2 2 4. 01 3 2 5. 6. 04 7. [2, 3) 8. 3 1, 2 ⎛⎞ ⎜⎟ ⎝⎠ 9. [–1, 0) 10. [–1, 8) 11. (– , 3) 12. ) 2, 13. f ( x ) = x 2 3 x f (0) = 0 2 3(0) = 0 f (5) = 5 2 3(5) = 25 15 = 10 f (3) = 3 2 3(3) = 9 9 = 0 f ( 7) = ( 7) 2 3( 7) = 49 + 21 = 70 14. f ( x ) = 9 6 x + x 2 f (0) = 9 6(0) + 0 2 = 9 0 + 0 = 9 f (2) = 9 6(2) + 2 2 = 9 12 + 4 = 1 f = 9 6(3) + 3 2 = 9 18 + 9 = 0 2 (1 3 ) 9 6 3 ) (1 3 ) 9 78 169 256 f −= −−+ =+ + = 15. f ( x ) = x 3 + x 2 x 1 f (1) = 1 3 + 1 2 1 1 = 0 f ( 1) = ( 3 + ( 2 ( 1 = 0 32 11 1 1 1 22 2 2 f ⎛⎞⎛⎞ ⎛⎞ ⎛⎞ 9 8 = +−− = ⎜⎟⎜⎟ ⎜⎟ ⎜⎟ ⎝⎠⎝⎠ ⎝⎠ ⎝⎠ f ( a ) = a 3 + a 2 a 1 16. g ( t ) = t 3 3 t 2 + t g (2) = 2 3 3( 2) 2 + 2 = 8 12 + 2 =− 2 11 1 3 22 2 g ⎛⎞ ⎛⎞⎛⎞ − −− + ⎜⎟ ⎜⎟⎜⎟ ⎝⎠ ⎝⎠⎝⎠ 1 2 1 8 3 4 1 2 11 8 2 2 3 33 3 3 g ⎛⎞⎛⎞ ⎛⎞ ⎛⎞ =− + ⎜⎟⎜⎟ ⎜⎟ ⎜⎟ ⎝⎠⎝⎠ ⎝⎠ ⎝⎠ = 8 27 12 9 + 2 3 10 27 g ( a ) = a 3 3 a 2 + a 17. h ( s ) = s + s ) () 3 1 21 h 3 = == + 3 1 3 3 h −− +− = h ( a + = a + 1 1 + ( a + = a + 1 a + 2 18. f ( x ) = x 2 x 2 1 2 1 1 2 4 2 1 1 4 2 1 f 3 = 2 1 1 2 4 2 1 1 4 2 1 f 3 = ⎝⎠−− f ( a + = ( a + 2 ( a + 2 1 = a 2 + 2 a + 1 ( a 2 + 2 a + 1 = a 2 + 2 a + 1 a 2 + 2 a 1

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Chapter 0: Functions ISM: Calculus & Its Applications, 11e 2 19. f ( x ) = x 2 2 x f ( a + 1) = ( a + 2 2( a + = ( a 2 + 2 a + 2 a 2 = a 2 1 f ( a + 2) = ( a + 2) 2 2( a + 2) = ( a 2 + 4 a + 4) 2 a 4 = a 2 + 2 a 20. f ( x ) = x 2 + 4 x + 3 f ( a = ( a 2 + 4( a + 3 = ( a 2 2 a + + (4 a 4) + 3 = a 2 + 2 a f ( a 2) = ( a 2) 2 + 4( a 2) + 3 = ( a 2 4 a + 4) + a 8) + 3 = a 2 1 21. a. f (0) represents the number of fax machines sold in 1990. b. f (2) = 50 + 4(2) + 1 2 (2) 2 = 50 + 8 + 2 = 60 22. R ( x ) = 100 b + x , x 0 a. b = 20, x = 60 R (60) = 100(60) 20 + 60 = 75% b. If R (50) = 60, then 60 = 100(50) b + 50 60 b + 3000 = 5000 100 3 b = 23. f ( x ) = 8 x ( x 1)( x 2) all real numbers except 1 and 2 24. 1 () ft t = all real numbers t > 0 25. 1 3 gx x = all real numbers x < 3 26. g ( x ) = 4 x ( x + 2) all real numbers x 0, –2 27. function 28. not a function 29. not a function 30. not a function 31. not a function 32. function 33. 1 34. –1 35. 3 36. 0 37. positive 38. negative 39. positive 40. yes 41. –1, 5, 9 42. –1 x 5, x 9 43. .03 44. .03 45. .04 46. 3 47. 1 2 2 fx x x ⎛⎞ = −+ ⎜⎟ ⎝⎠ 12 (3) 3 (3 2) 22 f =− += 5 Thus, (3, 12) is not on the graph. 48. f ( x ) = x (5 + x )(4 – x ) f (–2) = –2(5 + (–2))(4 – (–2)) = –36 So (–2, 12) is not on the graph. 49. g ( x ) = 3 x 1 x 2 + 1 ( ) 1 1 2 2 2 5 1 4 2 31 35 1 g = == + So , 25 is on the graph.
ISM: Calculus & Its Applications, 11e Chapter 0: Functions 3 50. g ( x ) = ( x 2 + 4) ( x + 2) () 2 2 40 3 9 8 2 33 4 25 32 g + ⎛⎞ == ⎜⎟ + ⎝⎠ 3 = So , is on the graph. 51. f ( x ) = x 3 f ( a + 1) = ( a + 3 52. 5 fx x x =− f (2 + h ) = 5 + h ) + h ) 22 5( 2 ) 14 ) 2 hh −+ − − ++ h 53. for 0 2 1f o r 2 xx ≤< = +≤ 5 (1) 1 1 f f (2) = 1 + 2 = 3 f (3) = 1 + 3 = 4 54. f ( x ) = 1 x for 1 x 2 x 2 for 2 < x f = 1 1 = 1 f (2) = 1 2 f (3) = 3 2 = 9 55.

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chapter 0 - Chapter 0 Exercises 0.1 1 2 3 4 5 6 7[2 3 3 8 1...

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