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In parts (a) and (b), use the given figure. (a) Solve the equation: f(x) = g(x). (b) Solve the inequality g(x) s f(x)

In parts (a) and (b), use the given figure. (a) Solve the equation: f(x) = g(x). (b) Solve the inequality g(x) s f(x)

Calculus: Early Transcendentals
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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Solve f(x)=g(x) And solve the inequality g(x)
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.
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: --- **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.
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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