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
Solve f(x)=g(x)
And solve the inequality g(x)

Transcribed Image Text:In parts (a) and (b), use the given figure.
(a) Solve the equation: \( f(x) = g(x) \).
(b) Solve the inequality \( g(x) \leq f(x) < h(x) \).
### Graph Explanation:
The graph displays three linear functions: \( y = f(x) \), \( y = g(x) \), and \( y = h(x) \).
- **Function \( y = f(x) \)**: This line passes through the points \((-11, -6)\) and intersects the line \( y = g(x) \) at \((0, -6)\).
- **Function \( y = g(x) \)**: This line also goes through the point \((0, -6)\) and intersects the line \( y = h(x) \) at \((6, 8)\).
- **Function \( y = h(x) \)**: This line is horizontal at \( y = 8\) and intersects the other lines at \((0, 8)\) and \((6, 8)\).
The intersections are key to solving the equation and inequality.
![Certainly! Here is the transcription suitable for an educational website:
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**Problem Set: Function Analysis**
**(a) For what value of x does \( f(x) = g(x) \)?**
\[ x = \, \_\_ \]
**(b) For which values of x is \( g(x) \leq f(x) < h(x) \)?**
*For every \( x \) in the interval \( \, \_\_ \, \), \( g(x) \leq f(x) < h(x) \).*
*(Type your answer in interval notation.)*
---
This prompt asks students to find specific values and intervals for which given conditions regarding the functions \( f(x) \), \( g(x) \), and \( h(x) \) hold true.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc01ef12d-4950-4fb4-b8ea-d8f1b4af58cd%2F93302bc4-1a62-4616-957f-6d5099803c61%2Fhf95jv_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Certainly! Here is the transcription suitable for an educational website:
---
**Problem Set: Function Analysis**
**(a) For what value of x does \( f(x) = g(x) \)?**
\[ x = \, \_\_ \]
**(b) For which values of x is \( g(x) \leq f(x) < h(x) \)?**
*For every \( x \) in the interval \( \, \_\_ \, \), \( g(x) \leq f(x) < h(x) \).*
*(Type your answer in interval notation.)*
---
This prompt asks students to find specific values and intervals for which given conditions regarding the functions \( f(x) \), \( g(x) \), and \( h(x) \) hold true.
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