Functions f and g are given as follows. X 5 X+2 x + 2 Find each of the following functions and state its domain. (a) f+g (b) f-g (c) f.g f(x) = g(x) = (d) Ⓡ 0714
Functions f and g are given as follows. X 5 X+2 x + 2 Find each of the following functions and state its domain. (a) f+g (b) f-g (c) f.g f(x) = g(x) = (d) Ⓡ 0714
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...
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![### Functions Overview
Functions \( f \) and \( g \) are given as follows:
\[ f(x) = \frac{5}{x+2} \]
\[ g(x) = \frac{x}{x+2} \]
### Tasks
Find each of the following functions and state its domain:
**(a)** \( f + g \)
**(b)** \( f - g \)
**(c)** \( f \cdot g \)
**(d)** \( \frac{f}{g} \)
**(e)** \( \frac{g}{f} \)
### Explanation
Each operation combines the functions \( f \) and \( g \) in different ways, either by addition, subtraction, multiplication, or division. The domain for each function should be determined by identifying any restrictions on the variable \( x \) that would make the denominator zero, leading to undefined values.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc8f23c41-b0a2-4b7f-b455-de9ffcd4a71a%2F66b367b9-b517-4645-8ea7-90ba0c968e2a%2Fd7olhc_processed.png&w=3840&q=75)
Transcribed Image Text:### Functions Overview
Functions \( f \) and \( g \) are given as follows:
\[ f(x) = \frac{5}{x+2} \]
\[ g(x) = \frac{x}{x+2} \]
### Tasks
Find each of the following functions and state its domain:
**(a)** \( f + g \)
**(b)** \( f - g \)
**(c)** \( f \cdot g \)
**(d)** \( \frac{f}{g} \)
**(e)** \( \frac{g}{f} \)
### Explanation
Each operation combines the functions \( f \) and \( g \) in different ways, either by addition, subtraction, multiplication, or division. The domain for each function should be determined by identifying any restrictions on the variable \( x \) that would make the denominator zero, leading to undefined values.
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