Find fog and go f. f(x)=√x+2, g(x) = x² (a) fog (b) gof Find the domain of each function and each composite function. (Enter your answers using interval notation.) domain of f domain of g domain of f o g domain of g of Need Help? Read It
Find fog and go f. f(x)=√x+2, g(x) = x² (a) fog (b) gof Find the domain of each function and each composite function. (Enter your answers using interval notation.) domain of f domain of g domain of f o g domain of g of Need Help? Read It
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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![# Composite Functions and Domain Determination
## Problem Statement
**Objective:** Find \( f \circ g \) and \( g \circ f \).
Given the functions:
\[ f(x) = \sqrt{x + 2}, \quad g(x) = x^2 \]
1. Determine \( f \circ g \)
2. Determine \( g \circ f \)
## Steps to Find the Composition of Functions
### (a) \( f \circ g \)
\[ f \circ g \]
### (b) \( g \circ f \)
\[ g \circ f \]
## Domain Analysis
Find the domain of each function and each composite function. (Enter your answers using interval notation.)
1. Domain of \( f \)
\[ \text{domain of } f \]
2. Domain of \( g \)
\[ \text{domain of } g \]
3. Domain of \( f \circ g \)
\[ \text{domain of } f \circ g \]
4. Domain of \( g \circ f \)
\[ \text{domain of } g \circ f \]
## Additional Resources
If you need further assistance, click the "Read It" button below.
[Need Help? Read It]
---
This covers the problem of finding the composition of two functions and determining their domains. This is often covered in pre-calculus or calculus courses. The functions provided are basic algebraic functions and the problem includes checking the domain of these composite functions to ensure they are correctly defined.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff2367e66-1ae4-4371-aa7b-db391deab840%2F55400834-2896-4a4f-9a8e-f72a1407eac7%2F197xsek_processed.png&w=3840&q=75)
Transcribed Image Text:# Composite Functions and Domain Determination
## Problem Statement
**Objective:** Find \( f \circ g \) and \( g \circ f \).
Given the functions:
\[ f(x) = \sqrt{x + 2}, \quad g(x) = x^2 \]
1. Determine \( f \circ g \)
2. Determine \( g \circ f \)
## Steps to Find the Composition of Functions
### (a) \( f \circ g \)
\[ f \circ g \]
### (b) \( g \circ f \)
\[ g \circ f \]
## Domain Analysis
Find the domain of each function and each composite function. (Enter your answers using interval notation.)
1. Domain of \( f \)
\[ \text{domain of } f \]
2. Domain of \( g \)
\[ \text{domain of } g \]
3. Domain of \( f \circ g \)
\[ \text{domain of } f \circ g \]
4. Domain of \( g \circ f \)
\[ \text{domain of } g \circ f \]
## Additional Resources
If you need further assistance, click the "Read It" button below.
[Need Help? Read It]
---
This covers the problem of finding the composition of two functions and determining their domains. This is often covered in pre-calculus or calculus courses. The functions provided are basic algebraic functions and the problem includes checking the domain of these composite functions to ensure they are correctly defined.
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