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(a) For what value of x does f(x) = g(x)? X= (b) For which values of x is f(x) > g(x)? For every x in the interval f(x) > g(x). (Type your answer in interval notation.)

(a) For what value of x does f(x) = g(x)? X= (b) For which values of x is f(x) > g(x)? For every x in the interval f(x) > g(x). (Type your answer in interval notation.)

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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The image shows a Cartesian coordinate plane with two intersecting lines, labeled as \( y = f(x) \) and \( y = g(x) \). The x-axis is labeled 'x' and the y-axis is labeled 'y'. - **Line \( y = f(x) \):** This line has a negative slope and intersects the other line. - **Line \( y = g(x) \):** This line has a positive slope. The point of intersection between the two lines is marked at the coordinates \((-7, 6)\). ### Explanation of the Graph: 1. **Axes**: The graph includes a horizontal x-axis and a vertical y-axis, both extending infinitely in their respective directions. 2. **Intersection Point**: The two lines intersect at the point \((-7, 6)\). This point is crucial as it represents the solution to the system of equations given by \( f(x) \) and \( g(x) \). This graph can be used to visually solve the system of linear equations by identifying where the two lines intersect on the coordinate plane.
Transcribed Image Text:The image shows a Cartesian coordinate plane with two intersecting lines, labeled as \( y = f(x) \) and \( y = g(x) \). The x-axis is labeled 'x' and the y-axis is labeled 'y'. - **Line \( y = f(x) \):** This line has a negative slope and intersects the other line. - **Line \( y = g(x) \):** This line has a positive slope. The point of intersection between the two lines is marked at the coordinates \((-7, 6)\). ### Explanation of the Graph: 1. **Axes**: The graph includes a horizontal x-axis and a vertical y-axis, both extending infinitely in their respective directions. 2. **Intersection Point**: The two lines intersect at the point \((-7, 6)\). This point is crucial as it represents the solution to the system of equations given by \( f(x) \) and \( g(x) \). This graph can be used to visually solve the system of linear equations by identifying where the two lines intersect on the coordinate plane.
**Question:** (a) For what value of \( x \) does \( f(x) = g(x) \)? - \( x = \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ \) (b) For which values of \( x \) is \( f(x) > g(x) \)? - For every \( x \) in the interval \(\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\), \( f(x) > g(x) \). *(Type your answer in interval notation.)*
Transcribed Image Text:**Question:** (a) For what value of \( x \) does \( f(x) = g(x) \)? - \( x = \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ \) (b) For which values of \( x \) is \( f(x) > g(x) \)? - For every \( x \) in the interval \(\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\), \( f(x) > g(x) \). *(Type your answer in interval notation.)*
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