Question

Identify the errors made in finding the inverse of y = x2 + 12x.



Describe the three errors.

Answer 1

The student did not switch both instances of x with y. He should have written x = y2 + 12y.He wrote only the principal square root instead of using the ± sign.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.

Answer 2

The inverse of a function is the opposite of the function.

The errors made are:

• The variables y and x are not properly swapped
• The square root should include the ± sign
• The domain of the function is incorrect, because x must be less than 0 for the radicand to have a real value

The function is given as:

$\mathbf{y = x^2 + 12x}$

The first error is that:

The variables are not properly swapped.

The proper expression should be

$\mathbf{x = y^2 + 12y}$

The next error is:

$\mathbf{y = \sqrt{-11x}}$

The correct expression is:

$\mathbf{y = \pm\sqrt{-11x}}$

Lastly, the domain is not correct.

Because if x is 0 or positive, $\mathbf{y = \sqrt{-11x}}$ will not have a real value.

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