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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 errors.

Sagot :

MrRoyal

The errors made by the student are:

  • The variables y and x are not properly swapped
  • The square root should include the ± sign
  • The domain of the function is incorrect

How to identify the errors?

The equation is given as:

[tex]y = x^2 + 12x[/tex]

The first step of the student is given as:

[tex]x = y^2 + 12x[/tex]

This is incorrect because the variables x and y must be completely swapped.

So, the actual step is [tex]x = y^2 + 12y[/tex]

The second step is given as:

[tex]y^2 = x - 12x[/tex]

The third step is given as:

[tex]y^2 = - 11x[/tex]

The last step is given as:

[tex]y = \sqrt{-11x}[/tex] for [tex]x \ge 0[/tex]

This is incorrect because [tex]y = \sqrt{-11x}[/tex]  would have complex solution for [tex]x \ge 0[/tex] and the square root needs to have a ±

Read more about inverse functions at:

https://brainly.com/question/14796161

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