Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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I have attached my answers and I was wondering if they are correct
Transcribed Image Text:1. Given that f(x) = {(1, 3), (2, 9), (5, 7), (11, 9)} and g(x) =
{(2,8), (3, 1), (4, 5), (9, 1), (11, 0)}
Determine the following.
a. f + g(x)
b. g(x)-f(x)
c. fx g(x)
f(x)
d.
g(x)
e. fog(x)
![Given that f(x) = {(1,3), (2, 9), (5, 7), (11, 9)}
And g(x) {(2, 8), (3, 1), (4, 5), (9, 1), (11, 0)}
We can write it as f: A → B
then A = {1, 2, 5, 11} and B = {3, 9, 7, 9}
g: CD then C = {2, 3, 4, 9, 11} and D = {8, 1, 5, 1, 0}
Then An C = {2,11}
So (f + g)(x), g(x) − f(x), (f × g)(x), f(x)g(x), (f o g)(x)
Defined on {2, 11}
a. f(x) + g(x)
On {2, 11}
f(2) + g(2) = 9+ 8 = 17
f(11) + g(11) = 9 + 0 = 9
Therefore, f(x) + g(x) = {(2,17), (11,9)}
b. g(x) = f(x)
On {2, 11}
g(11) f(11) = 0 - 9 = 9
Therefore, g(x) = f(x) = {(2,
-
c. f(x) x g(x)
On {2,11}
1),
- 1), (11,
(11, — 9)}
f(2) × g(2) = 9 x 8 = 72
f(11) × g(11) = 9 x 0 = 0
Therefore, f(x) x g(x) = {(2,72), (11, 0)}
d. f(x)g(x)
=
On {2, 11}
f(2)g(2) = 9(8) = 72
f(11)g(11) = 9x0=0
Therefore, f(x) g(x) = {(2,72), (11, 0)}
e. (fog)(2) = f[g(2)] = ƒ(8) = þ
(fog)(11) = f[g(11)] = f(0) = $
Therefore, (fog)(x) {4}](https://content.bartleby.com/qna-images/question/bec23eaa-92f3-4f87-87f5-5f749f4e6e2d/bef0b244-a0d3-4759-bd95-fbed44214c55/ium5t99_processed.png)
Transcribed Image Text:Given that f(x) = {(1,3), (2, 9), (5, 7), (11, 9)}
And g(x) {(2, 8), (3, 1), (4, 5), (9, 1), (11, 0)}
We can write it as f: A → B
then A = {1, 2, 5, 11} and B = {3, 9, 7, 9}
g: CD then C = {2, 3, 4, 9, 11} and D = {8, 1, 5, 1, 0}
Then An C = {2,11}
So (f + g)(x), g(x) − f(x), (f × g)(x), f(x)g(x), (f o g)(x)
Defined on {2, 11}
a. f(x) + g(x)
On {2, 11}
f(2) + g(2) = 9+ 8 = 17
f(11) + g(11) = 9 + 0 = 9
Therefore, f(x) + g(x) = {(2,17), (11,9)}
b. g(x) = f(x)
On {2, 11}
g(11) f(11) = 0 - 9 = 9
Therefore, g(x) = f(x) = {(2,
-
c. f(x) x g(x)
On {2,11}
1),
- 1), (11,
(11, — 9)}
f(2) × g(2) = 9 x 8 = 72
f(11) × g(11) = 9 x 0 = 0
Therefore, f(x) x g(x) = {(2,72), (11, 0)}
d. f(x)g(x)
=
On {2, 11}
f(2)g(2) = 9(8) = 72
f(11)g(11) = 9x0=0
Therefore, f(x) g(x) = {(2,72), (11, 0)}
e. (fog)(2) = f[g(2)] = ƒ(8) = þ
(fog)(11) = f[g(11)] = f(0) = $
Therefore, (fog)(x) {4}
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