Answer The solution to the equation − x e − x + e − x = 0 are x = 1 _ Explanation Given information : − x e − x + e − x = 0 Concept Involved: The word “solve” means the process of finding the value of x that makes the equation true. In order to solve we need to undo whatever is done to x . The solution to the equation f ( x ) = g ( x ) graphically is the x value of the point of intersection of where the two graphs meet. Formula Used: Zero factor property: If a ⋅ b = 0 , then a = 0 ( o r ) b = 0 Calculation: Factor the Greatest Common Factor in the left side of the equation. − e − x ( x − 1 ) = 0 Use the zero factor property to set each factor to zero − e − x = 0 ▶ 1 s t equation x − 1 = 0 ▶2 n d equation Solving the equation e − x = 0 There is no value of x that makes the above equation TRUE, so No solution Solving the equation x − 1 = 0 By adding 1 on both sides, and then By Simplifying on both sides x − 1 + 1 = 0 + 1 x = 1 Check for extraneous solution by substituting the result in the original equation. x = 1 makes the original equation TRUE. Graph: Interpretation: Setting up left side of the equation f ( x ) = − x e − x + e − x and right side of the equation g ( x ) = 0 . The xcoordinate of point of intersection of two graphs is the solution to the equation − x e − x + e − x = 0 Conclusion: The solution to the equation − x e − x + e − x = 0 are x = 1 _

4th Edition

ISBN: 9781337516853

Author: Larson

Publisher: CENGAGE CO

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Question

Chapter 3.4, Problem 75E

To determine

To find : solution to the equation algebraically and verify the result graphically.

Expert Solution & Answer

Answer to Problem 75E

The solution to the equation −xe−x+e−x=0 are x=1 _

Explanation of Solution

Given information: −xe−x+e−x=0

Concept Involved:

The word “solve” means the process of finding the value of x that makes the equation true. In order to solve we need to undo whatever is done to x . The solution to the equation f(x)=g(x) graphically is the x value of the point of intersection of where the two graphs meet.

Formula Used:

Zero factor property: If a⋅b=0 , then a=0 (or) b=0

Calculation:

Factor the Greatest Common Factor in the left side of the equation.

−e−x(x−1)=0

Use the zero factor property to set each factor to zero

−e−x=0▶ 1^s^tequation

x−1=0▶2ⁿ^dequation

Solving the equation e−x=0

There is no value of x that makes the above equation TRUE, so No solution

Solving the equation x−1=0

By adding 1 on both sides, and then
By Simplifying on both sides

x−1+1=0+1

x=1

Check for extraneous solution by substituting the result in the original equation.

x=1 makes the original equation TRUE.

Graph:

EBK PRECALCULUS W/LIMITS, Chapter 3.4, Problem 75E

Interpretation:

Setting up left side of the equation f(x)=−xe−x+e−x and right side of the equation g(x)=0 .

The xcoordinate of point of intersection of two graphs is the solution to the equation −xe−x+e−x=0

Conclusion:

The solution to the equation −xe−x+e−x=0 are x=1 _

Chapter 3.4, Problem 74E

Chapter 3.4, Problem 76E

Chapter 3 Solutions

EBK PRECALCULUS W/LIMITS

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