Mathematics : asked on kidward
 21.06.2022

Identify the errors made in finding the inverse of y = x2 + 12x. an image shows a student's work. line 1 is x = y squared + 12 x. line 2 is y squared = x minus 12 x. line 3 is y squared = negative 11 x. line 4 is y = startroot negative 11 x endroot, for x greater-than-or-equal 0. describe the three erro

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Step-by-step answer

17.02.2022, solved by verified expert
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47 students found this answer . helpful

The three mistakes are:

1) Interchanging the variable x and y is incorrect.

2) Student need to use ± sign.

3) The domain of the function is incorrect it should be x ≤ 0.

Step-by-step explanation:

Consider the provided steps.

Identify the errors made in finding the inverse, №15221295, 21.06.2022 07:03

Step 1: Identify the errors made in finding the inverse, №15221295, 21.06.2022 07:03

The first step is wrong interchanging the variable x and y should be:

Identify the errors made in finding the inverse, №15221295, 21.06.2022 07:03

Step 2: Identify the errors made in finding the inverse, №15221295, 21.06.2022 07:03

Step 3: Identify the errors made in finding the inverse, №15221295, 21.06.2022 07:03

Step 4: Identify the errors made in finding the inverse, №15221295, 21.06.2022 07:03, for x≥0

The step 4 is wrong because student need to use ± sign. The another mistake is the domain of the function is incorrect.

Because the radicand should be greater or equal to 0.

For which x must be less than or equal to zero. It should be x ≤ 0.

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32 students found this answer . helpful

Sample 1.The student did not switch both instances of x with y. He should have written x = y2 + 12y.

2.He wrote only the principal square root instead of using the ± sign.

3.The domain is incorrect. For the radicand to be greater than or equal to zero, x must be less than or equal to zero. It should be x ≤0.

Step-by-step explanation: For sure enjoy!

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StudenGPT
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P Answered by Studen AI
To identify the errors made in finding the inverse of the given equation y = x^2 + 12x, let's analyze each step of the student's work:

Line 1: x = y^2 + 12x

Error 1: In line 1, the student has mistakenly written the equation in terms of x instead of y. The equation should be y = x^2 + 12x, reflecting the original equation.

Line 2: y^2 = x - 12x

Error 2: In line 2, the student attempted to isolate y but made an error when distributing the subtraction of 12x. The equation should be y^2 = x - 12x = -11x instead of y^2 = x - 12x.

Line 3: y^2 = -11x

Error 3: In line 3, the student correctly eliminated the x term, but falsely placed a negative sign in front of the 11 instead of the x term. The equation should be y^2 = 11x, not y^2 = -11x.

Line 4: y = √(-11x), for x ≥ 0

No errors were identified in this step. However, it's important to note that to obtain the inverse function, we need to switch the roles of x and y. Therefore, the correct expression should be x = √(-11y), for y ≥ 0.

In summary, the errors made by the student are as follows:
1. Writing the equation in terms of x instead of y.
2. Distributing the subtraction of 12x incorrectly.
3. Incorrectly placing the negative sign in front of the x term.
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P=2000

R=1.5

T=6

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where y=Value of coin

x=Age in years

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The answer is in the image 

The answer is in the image 

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here,

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Cost before sale tax=$46.00

Cost after including tax=$48.76

Sale tax=$48.76-46.00

=$2.76

we know,

sale tax=((sales tax rate)/100) * cost before sale tax

2.76=((sales tax rate)/100) *46.00

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Cost of 1 gallon =15/6

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