Question

Explain the mistake that is made. Given the functions $f(x)=|x-A|-1$ and $f(1)=-1,$ find $A$. Solution: Since $f(1)=-1,$ the point (-1,1) $-1=|-1-A|-1$ Add 1 to both sides of the equation. $|-1-A|=0$ The absolute value of zero is zero, so there is no need for the absolute value signs: $-1-A=0 \Rightarrow A=-1$. This is incorrect. What mistake was made?

Name: Problem 126, Chapter 3: Algebra and Trigonometry
Uploaded: 2021-06-23T02:06:20-08:00
Duration: 1 min 40 s
Channel: Melissa Barry
Description: Explain the mistake that is made. Given the functions f(x)=|x-A|-1 and f(1)=-1, find A. Solution: Since f(1)=-1, the point (-1,1) -1=|-1-A|-1 Add 1 to both sides of the equation. |-1-A|=0 The absolute value of zero is zero, so there is no need for the absolute value signs: -1-A=0 ⇒A=-1. This is incorrect. What mistake was made?

   Explain the mistake that is made.
Given the functions $f(x)=|x-A|-1$ and $f(1)=-1,$ find $A$.
Solution:
Since $f(1)=-1,$ the point (-1,1)
$-1=|-1-A|-1$
Add 1 to both sides of the equation.
$|-1-A|=0$
The absolute value of zero is zero, so there is no need for the absolute value signs: $-1-A=0 \Rightarrow A=-1$. This is incorrect. What mistake was made?

Algebra and Trigonometry

Cynthia Y. Young 4th Edition

Chapter 3, Problem 126

Instant Answer

Solved by Expert Melissa Barry

06/23/2021

Step 1

This means that when we substitute $x=1$ into the function $f(x)$, the result is $-1$. So, we write the equation as $-1=|1-A|-1$. Show more…

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Explain the mistake that is made. Given the functions $f(x)=|x-A|-1$ and $f(1)=-1,$ find $A$. Solution: Since $f(1)=-1,$ the point (-1,1) $-1=|-1-A|-1$ Add 1 to both sides of the equation. $|-1-A|=0$ The absolute value of zero is zero, so there is no need for the absolute value signs: $-1-A=0 \Rightarrow A=-1$. This is incorrect. What mistake was made?

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Key Concepts

Function Evaluation

Understanding function evaluation is crucial. It involves substituting the input value correctly into the function's expression. In problems like this, misidentifying the input value (e.g., using a wrong value) can lead to an incorrect equation and a consequent error in the solution.

Absolute Value Properties

The absolute value function has specific properties, notably that the absolute value of an expression equals zero only if the expression itself is zero. Correctly applying this property is essential when solving equations involving absolute values, but doing so requires accurate setup of the equation.

Algebraic Substitution Error

Proper substitution is key in replacing the variable with the provided value, ensuring that the resulting equation accurately reflects the given conditions. The error in the solution arose from an incorrect substitution, where the wrong input value was used, leading to an incorrect equation and faulty conclusion.

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