31. y = x 3 3 X Doma -3

Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
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Chapter4: Exponential And Logarithmic Functions
Section4.1: Exponential Functions
Problem 8E
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276 CHAPTER 5 Exponential and Logarithmic Functions
In Problems 43–54, the function f is one-to-one. (a) Find its inverse function f-1 and check your answer. (b) Find the domain and the ronge
25.
24.
3 x
-3
3 X
-3
* 7ooiems 27-32, the graph of a one-to-one function fis given. Draw the graph of the inverse function f¯'.
27.
29.
y = x
y = *
28.
y = x
(1, 2)
VistuF/(2, 1)
(0, 1).
(2, )
-3
(-1, 0)
lo d3
(-1, –1) En
3 x
(1, 0)
-3
|(0,-1)
(-2, -2)
(-2, -2)
-3-
-3-
-3-
32.
y = x
30.
31.
y = x
3
(-2, 1)
3 x
(1,-1)
A e 2 x
lo gT orl oe odi alo ni
-3
3 x -2
-3F
-3
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 an
values of x that need to be excluded from the domain of f and the domain of g.
33. f(x) = 3x + 4; g(x) = -(x – 4)
34. f(x) = 3 – 2x; g(x) = -
:- 3)
35. f(x) = 4x – 8; g(x) = + 2
36. f(x) = 2x + 6; g(x) = ,x – 3
37. f(x) = x³ - 8; g(x) = Vx + 8
38. f(x) = (x – 2)²,x = 2; g(x) = Vx + 2
39. f(x) =
= 8(x) =
40. f(x) = x; g(x) = x
41. f(x) =
2x + 3
4x - 3
g(x) =
x + 4*
2 - x
x - 5
2x + 3' 8(x)
42. f(x)
3x + 5
ancd
1 - 2x
of f and f. (c) Graph f, f", and y = x on the same coordinate axes
43. f(x) = 3x
44. f(x) = -4x
46. f(x) = 1 – 3x
47. f(x) = x - 1
45. f(x) = 4x + 2
49. f(x) = x + 4, x20
50. f(x) = x + 9, x 2 0
48. f(x) = x³ + 1
52. f(x) = -
4
51. f(x) =
53. f(x)
:2
Transcribed Image Text:276 CHAPTER 5 Exponential and Logarithmic Functions In Problems 43–54, the function f is one-to-one. (a) Find its inverse function f-1 and check your answer. (b) Find the domain and the ronge 25. 24. 3 x -3 3 X -3 * 7ooiems 27-32, the graph of a one-to-one function fis given. Draw the graph of the inverse function f¯'. 27. 29. y = x y = * 28. y = x (1, 2) VistuF/(2, 1) (0, 1). (2, ) -3 (-1, 0) lo d3 (-1, –1) En 3 x (1, 0) -3 |(0,-1) (-2, -2) (-2, -2) -3- -3- -3- 32. y = x 30. 31. y = x 3 (-2, 1) 3 x (1,-1) A e 2 x lo gT orl oe odi alo ni -3 3 x -2 -3F -3 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 an values of x that need to be excluded from the domain of f and the domain of g. 33. f(x) = 3x + 4; g(x) = -(x – 4) 34. f(x) = 3 – 2x; g(x) = - :- 3) 35. f(x) = 4x – 8; g(x) = + 2 36. f(x) = 2x + 6; g(x) = ,x – 3 37. f(x) = x³ - 8; g(x) = Vx + 8 38. f(x) = (x – 2)²,x = 2; g(x) = Vx + 2 39. f(x) = = 8(x) = 40. f(x) = x; g(x) = x 41. f(x) = 2x + 3 4x - 3 g(x) = x + 4* 2 - x x - 5 2x + 3' 8(x) 42. f(x) 3x + 5 ancd 1 - 2x of f and f. (c) Graph f, f", and y = x on the same coordinate axes 43. f(x) = 3x 44. f(x) = -4x 46. f(x) = 1 – 3x 47. f(x) = x - 1 45. f(x) = 4x + 2 49. f(x) = x + 4, x20 50. f(x) = x + 9, x 2 0 48. f(x) = x³ + 1 52. f(x) = - 4 51. f(x) = 53. f(x) :2
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