- 432 Chapter 6 Exponential And Logarithmic Functions 24 Y 30 2 Y X 1 2 0 1 J 1 0 3 3 X 2 2 3 2 1 1 (78.74 KiB) Viewed 16 times
432 CHAPTER 6 Exponential and Logarithmic Functions 24. y 30. 2 y = x (1, 2) (0, 1) J (-1,0) -3 3 X (-2,-2) 3 (-2, 1). * -3 3 x (1.-1) In Problems 27-32, the graph of a one-to-one function fis given. Draw the graph of the inverse function f-¹. 27. 28. 29. 33. f(x) = 3x + 4; 35. f(x) = 4x - 8; 37. f(x) = x³-8; g(x) = (x-4) g(x) == + 2 g(x)=√x + 8 g(x) == 39. f(x) = 41. f(x) = 2x+2. 3 g(x) = 46. f(x) = 13x 49. f(x) = x² + 4, x=0 25. 52. f(x) = - ³ 4x3 y = x (2, 3) J -3 (1,0) 3x (-2,-2) (0, -1) -3 31. y = x 26. -3 32. 47. f(x) = x³ - 1 50. f(x) = x² + 9, xz0 53. f(x) = x=2 In Problems 33-42, verify that the functions f and g are inverses of each other by showing that f(g(x)) = x and g(f(x)) = x. Give any values of x that need to be excluded from the domain of f and the domain of g. 34. f(x) = 32x; g(x) = = -1/(x-3) 36. f(x) = 2x + 6: g(x) = x-3 38. f(x) = (x - 2)² x ≥ 2; 40. f(x)=x: g(x) = x 3x + 5 42. f(x) = ²x+3² 8(x) = 1 - 2x 2x 3b -3 (-1,-1) K Z -3 In Problems 43-54, the function fis one-to-one. (a) Find its inverse function f and check your answer. (b) Find the domain and the range off and f-¹. (c) Graph f, f-1, and y = x on the same coordinate axes. 43. f(x) = 3x 44. f(x) = -4x y=x (2, 1) 45. f(x) = 4x + 2 48. f(x) = x³ + 1 g(x)=√x + 2 51. f(x) = 3 x 54. f(x) = x+2