1. True or False. On the space provided, write T if the statement is true and F if otherwise. 1 T I 144 LL Exercises 1.3 T 1. For any functions f and g, (f + g) (x) = (g + f)(x). 2. For any functions fand g, (f.g)(x) = (g•f)(x). 3. If for any functions f and g, (fog)(x) = (gof)(x), then fand g are inverses of each other. 4. The composite function (fog)(x) is always equal to (gof)(x) for functions fand g. 5. The value of (fog) (2) is sometimes equal to (gof) (2) for functions fand g. F 9. 6. The domain off-g is the domain common to f and g. The domain off + g is the domain common to f and g. 7. 8. Then, the domain of 1 Suppose g(x) = x - 1 and f(x) =. (fog)(x) is R - {1}. x If g(x) = x - 1 and f(x) = = for x = 0 and x 1. 10. If g(x) = x - 1 and f(x) = =-=- for x = 0 and x # 1. then (-/-)(x) = 1, then II. Find the sum of all given functions. 1. f(x) = 2x and g(x)=x-4 3x-4 2. f(x)=x² + 3x - 5 and g(x)=x²+4 2x² + 3x-1 3. f(x)=√x +3 and g(x) = x² + 2√x -1x²/3√x+2 4. f(x) = *+2 Y²4 y², 2 x²-x
1. True or False. On the space provided, write T if the statement is true and F if otherwise. 1 T I 144 LL Exercises 1.3 T 1. For any functions f and g, (f + g) (x) = (g + f)(x). 2. For any functions fand g, (f.g)(x) = (g•f)(x). 3. If for any functions f and g, (fog)(x) = (gof)(x), then fand g are inverses of each other. 4. The composite function (fog)(x) is always equal to (gof)(x) for functions fand g. 5. The value of (fog) (2) is sometimes equal to (gof) (2) for functions fand g. F 9. 6. The domain off-g is the domain common to f and g. The domain off + g is the domain common to f and g. 7. 8. Then, the domain of 1 Suppose g(x) = x - 1 and f(x) =. (fog)(x) is R - {1}. x If g(x) = x - 1 and f(x) = = for x = 0 and x 1. 10. If g(x) = x - 1 and f(x) = =-=- for x = 0 and x # 1. then (-/-)(x) = 1, then II. Find the sum of all given functions. 1. f(x) = 2x and g(x)=x-4 3x-4 2. f(x)=x² + 3x - 5 and g(x)=x²+4 2x² + 3x-1 3. f(x)=√x +3 and g(x) = x² + 2√x -1x²/3√x+2 4. f(x) = *+2 Y²4 y², 2 x²-x
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
Related questions
Question
![Nam
Name of Tea
Grade/Section
1
1
|
Fif otherwise.
1. True or False. On the space provided, write T if the statement is true and
T
F
T
144
F
Exercises 1.3
1.
For any functions f and g, (f+ g)(x) = (g+f)(x).
2.
For any functions fand g, (f. g)(x) = (g•f)(x).
3.
If for any functions f and g, (fog)(x) = (g o f)(x), then
fand g are inverses of each other.
4.
The composite function (fog)(x) is always equal to
(gof)(x) for functions fand g.
6.
7.
8.
Score
5.
The value of (fog) (2) is sometimes equal to (gof) (2) for
functions fand g.
The domain off-g is the domain common to f and g.
The domain off + g is the domain common to f and g.
Then, the domain of
1
Suppose g(x) = x - 1 and f(x) =
(fog)(x) is R - {1}.
X
9. If g(x) = x - 1 and f(x) = -=-
for x = 0 and x 1.
- 10. If g(x) =
= x -
for x = 0 and x#1.
x - 1 and
f(x)
1 and f(x) = =
then
(-1)(x) = 21²-x
(-²)(x) =
then
II. Find the sum of all given functions.
1. f(x) = 2x and g(x)=x-4 3x-4
2. f(x)=x² + 3x - 5 and g(x) = x² +4 2x² + 3x-1
3. f(x)=√x +3 and g(x) = x² + 2√√x -1 X²-3√x+2
Y2
Y ²4 2
4. f(x) = x + 2
x-1](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fad6c908b-065b-4825-b690-db5d565cb29b%2F877b63d9-83ca-4197-8e60-7153f68fa63a%2Fmw5p3a_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Nam
Name of Tea
Grade/Section
1
1
|
Fif otherwise.
1. True or False. On the space provided, write T if the statement is true and
T
F
T
144
F
Exercises 1.3
1.
For any functions f and g, (f+ g)(x) = (g+f)(x).
2.
For any functions fand g, (f. g)(x) = (g•f)(x).
3.
If for any functions f and g, (fog)(x) = (g o f)(x), then
fand g are inverses of each other.
4.
The composite function (fog)(x) is always equal to
(gof)(x) for functions fand g.
6.
7.
8.
Score
5.
The value of (fog) (2) is sometimes equal to (gof) (2) for
functions fand g.
The domain off-g is the domain common to f and g.
The domain off + g is the domain common to f and g.
Then, the domain of
1
Suppose g(x) = x - 1 and f(x) =
(fog)(x) is R - {1}.
X
9. If g(x) = x - 1 and f(x) = -=-
for x = 0 and x 1.
- 10. If g(x) =
= x -
for x = 0 and x#1.
x - 1 and
f(x)
1 and f(x) = =
then
(-1)(x) = 21²-x
(-²)(x) =
then
II. Find the sum of all given functions.
1. f(x) = 2x and g(x)=x-4 3x-4
2. f(x)=x² + 3x - 5 and g(x) = x² +4 2x² + 3x-1
3. f(x)=√x +3 and g(x) = x² + 2√√x -1 X²-3√x+2
Y2
Y ²4 2
4. f(x) = x + 2
x-1
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Recommended textbooks for you
![Calculus: Early Transcendentals](https://www.bartleby.com/isbn_cover_images/9781285741550/9781285741550_smallCoverImage.gif)
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
![Thomas' Calculus (14th Edition)](https://www.bartleby.com/isbn_cover_images/9780134438986/9780134438986_smallCoverImage.gif)
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
![Calculus: Early Transcendentals (3rd Edition)](https://www.bartleby.com/isbn_cover_images/9780134763644/9780134763644_smallCoverImage.gif)
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
![Calculus: Early Transcendentals](https://www.bartleby.com/isbn_cover_images/9781285741550/9781285741550_smallCoverImage.gif)
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
![Thomas' Calculus (14th Edition)](https://www.bartleby.com/isbn_cover_images/9780134438986/9780134438986_smallCoverImage.gif)
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
![Calculus: Early Transcendentals (3rd Edition)](https://www.bartleby.com/isbn_cover_images/9780134763644/9780134763644_smallCoverImage.gif)
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
![Calculus: Early Transcendentals](https://www.bartleby.com/isbn_cover_images/9781319050740/9781319050740_smallCoverImage.gif)
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
![Precalculus](https://www.bartleby.com/isbn_cover_images/9780135189405/9780135189405_smallCoverImage.gif)
![Calculus: Early Transcendental Functions](https://www.bartleby.com/isbn_cover_images/9781337552516/9781337552516_smallCoverImage.gif)
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning