Question

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

Answer 1

Answer: Sample Answer: 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!

Answer 2

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.

Explanation:

Consider the provided steps.

`y = x^2 + 12x`

Step 1:
`x = y^2 + 12x`

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

`x=y^2+12y`

Step 2:
`y^2= x-12x`

Step 3:
`y^2= -11 x`

Step 4:
`y=√(-11x)`, 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.