Exercises 33 – 38 refer to the graphs of the functions
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Calculus & Its Applications (14th Edition)
- In Exercises 11–18, graph each function by making a table of coordinates. If applicable, use a graphing utility to confirm your hand-drawn graph. 11. f(x) = 4" 13. g(x) = ()* 15. h(x) = (})* 17. f(x) = (0.6) 12. f(x) = 5" 14. g(x) = () 16. h(x) = (})* 18. f(x) = (0.8)* %3!arrow_forwardEach of Exercises 25–36 gives a formula for a function y = f(x). In each case, find f-x) and identify the domain and range of f-. As a check, show that f(fx)) = f-"f(x)) = x. 25. f(x) = x 26. f(x) = x, x20 %3D %3D 27. f(x) = x + 1 28. f(x) = (1/2)x – 7/2 30. f(x) = 1/r, x * 0 %3D 29. f(x) = 1/x, x>0 x + 3 31. f(x) 32. f(x) = VE - 3 34. f(x) = (2x + 1)/5 2 33. f(x) = x - 2r, xs1 (Hint: Complete the square.) * + b x - 2' 35. f(x) = b>-2 and constant 36. f(x) = x? 2bx, b> 0 and constant, xsbarrow_forwardIn Exercises 16–22, show that the two functions are inverses of each other. 2 16. f(x) = 3x + 2 and g(x) = 3arrow_forward
- In Exercises 7–10,find the two x-intercepts of the function f andshow that f '(x) = 0 at some point between the twox-intercepts. f (x) = x2 − x − 2arrow_forwardUse Definition 0.10 to show that each pair of functions in Exercises 67–70 are inverses of each other. 1 2 67. f(x) =2 – 3x and g(x) = -x+ 3 68. f(x) = x² restricted to [0, 0) and g(x) = V 69. f(x) = and g(x) = 1+x 1-x 1 1 70. f(x) = and g(x) 2x 2xarrow_forwardIn Exercises 33–38, express the function, f, in simplified form. Assume that x can be any real number. 33. f(x) = V36(x + 2)² 34. f(x) = V81(x – 2)2 35. f(x) = V32(x + 2)³ 36. f(x) = V48(x – 2)³ 37. f(x) = V3x² – 6x + 3 38. f(x) = V5x2 – 10x + 5 %3Darrow_forward
- a) Find the domain of f, g, f + g, f – & fg, ff, f/ g b) Find (f + g)(x), (f – g)(x), (fg)(x), (ff)(x), For each pair of functions in Exercises 17–32: 15. (8 and g/f. Find f+ g)(x), (f – g)(x), (fg)(x), (ff)(x), (f/8)(x), and (g/f)(x). 17. f(x) = 2x + 3, g(x) = 3 – 5x %3D 18. f(x) = -x + 1, g(x) = 4x – 2 19. f(x) = x – 3, g(x) = Vx + 4 20. f(x) = x + 2, g(x) = Vx – 1 21. f(x) = 2x – 1, g(x) = – 2x² 22. f(x) = x² – 1, g(x) = 2x + 5 23. f(x) = Vx – 3, g(x) : = Vx + 3arrow_forwardExercises 63–86: Use transformations to sketch a graph of f. 63. f(x) = x² – 3 64. f(x) = -x² 65. f(x) = (x = 5)² + 3 66. f(x) = (x + 4)° 67. flx) = -Vx 68. f(x) = 2(x = 1F + 1 69. f(x) = -x² + 4 70. f(x) = V=x 71. f(x) = |x| – 4 73. f(x) = Vx – 3 + 2 74. f(x) = |x + 2| – 3 72. flx) = Vx + 1 76. flx) = |x| 78. f(x) = 2Vx – 2 - 1 75. f(x) = |2x| 77. f(x) = 1 – Vx 79. f(x) = -Vī - x 81. f(x) = V-(x + 1) 80. f(x) = V-x – 1 82. f(x) = 2 + V-(x – 3) 83. f(x) = (x = 1) 84. f(x) = (x + 2) 85. f(x) = -x' 86. f(x) = (-x)' + 1arrow_forwardIn Exercises 104–105, express the given function h as a composition of two functions f and g so that h(x) = (f• g)(x). 104. h(x) = (x² + 2x – 1)* 105. h(x) = V7x + 4 %3! %3!arrow_forward
- Graph the functions f(x) = xn for n = 1, 3, and 5 in a [-2, 2, 1] by [-2, 2, 1] viewing rectangle.arrow_forwardIn Exercises 39–44, each function f(x) changes value when x changes from x, to xo + dx. Find a. the change Af = f(xo + dx) – f(xo); b. the value of the estimate df = f'(xo) dx; and c. the approximation error |Af – df|. y = f(x)/ Af = f(xo + dx) – f(x) df = f'(xo) dx (xo, F(xo)) dx Tangent 0| xo + dx 39. f(x) 3D х? + 2x, хо —D 1, 40. f(x) = 2x² + 4x – 3, xo = -1, dx = 0.1 41. f(x) = x³ - x, xo = 1, dx = 0.1 dx = 0.1 %3D 42. f(x) 3 х, Хо —D 1, dx %3D 0.1 43. f(x) — х 1, Хо —D 0.5, dx %3D0.1 44. f(x) 3D х3 — 2х + 3, Хо — 2, dx 3D 0.1arrow_forwardIn Exercises 63–65, find the domain and range of each composite function. Then graph the composition of the two functions on separate screens. Do the graphs make sense in each case? Give reasons for your answers. Comment on any differences you see. 63. a. y = tan-1 (tan x) b. y = tan (tan-1 x) 64. a. y = sin-1 (sin x) b. y = sin (sin-1 x) 65. a. y = cos-1 (cos x) b. y = cos (cos-1 x)arrow_forward
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