52. f(x) (x)8 g(x) = 3x + 2 %3D 3. 54, f(x) = 2 – x², g(x) = V2 – x for x < 2 56. f(x) = (5 – x)½, g(x) = 5 – x³

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.5: Graphs Of Functions
Problem 50E
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Number 54 please. Instructions are in the 2nd photo. 

52. f(x)
(x)8
g(x) = 3x + 2
%3D
3.
54, f(x) = 2 – x², g(x) = V2 – x for x < 2
56. f(x) = (5 – x)½, g(x) = 5 – x³
Transcribed Image Text:52. f(x) (x)8 g(x) = 3x + 2 %3D 3. 54, f(x) = 2 – x², g(x) = V2 – x for x < 2 56. f(x) = (5 – x)½, g(x) = 5 – x³
|3|
42. J()
g(x) = x² + 5
.2
45. f(x) = Vx 1,
46. f(x) = Vx
1
g(x) =
1
47. f(x) =
x-3,
g(x)
x - 3
x² - 3'
|
48. JX)
2- x
x²
+ 2x + 1 50. f(x) = (1 – x²)2, g(x)
%3D
In Exercises 51--60, show that f(g(x)) = x and g(f(x)) = x.
X 1
e(x)
1
x - 2
f(x) = ² ,², g(x) = 3x + 2
%3D
3
53. f(x) = Vx 1,
= x + 1 for A = 1
%3D
|
54, f(x) = 2 – x², g(x) = V2 - x for x < 2
|
1
55. fl«) = - g(x) = - fo
1
for x + 0
%3D
%3D
56. f(x) = (5 – x)/3, g(x) = 5 – x³
%3D
Vx + 9
57 f(x) = 4x² – 9, g(x)
x³+1
%3D
for x > 0
58. f(x) = V8x – 1, g(x)
%3D
2
|
8.
1
X + 1
59. f(x)
g(x)
%3D
for x # 0, x # 1
60. f(x) = V25 – x², g(x) = V 25 – x² for
%3D
Transcribed Image Text:|3| 42. J() g(x) = x² + 5 .2 45. f(x) = Vx 1, 46. f(x) = Vx 1 g(x) = 1 47. f(x) = x-3, g(x) x - 3 x² - 3' | 48. JX) 2- x x² + 2x + 1 50. f(x) = (1 – x²)2, g(x) %3D In Exercises 51--60, show that f(g(x)) = x and g(f(x)) = x. X 1 e(x) 1 x - 2 f(x) = ² ,², g(x) = 3x + 2 %3D 3 53. f(x) = Vx 1, = x + 1 for A = 1 %3D | 54, f(x) = 2 – x², g(x) = V2 - x for x < 2 | 1 55. fl«) = - g(x) = - fo 1 for x + 0 %3D %3D 56. f(x) = (5 – x)/3, g(x) = 5 – x³ %3D Vx + 9 57 f(x) = 4x² – 9, g(x) x³+1 %3D for x > 0 58. f(x) = V8x – 1, g(x) %3D 2 | 8. 1 X + 1 59. f(x) g(x) %3D for x # 0, x # 1 60. f(x) = V25 – x², g(x) = V 25 – x² for %3D
Expert Solution
Step 1

Given that 

f(x) = 2 - x2

g(x) = 2-x,           x2

To show  that f(g(x)) = x

And g(f(x)) = x

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