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

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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 erro

Mathematics

2 answers:

zzz [12.3K] · Answer 1 · 2026-02-16T14:49:59+03:00

Answer: Sample response: 1. The student failed to replace both instances of x with y, and should have written x = y² + 12y.

2. Only the principal square root was expressed; the ± sign is missing.

3. The domain is incorrect; since the radicand must be at least zero, x must be less than or equal to zero, i.e., x ≤ 0.

Step-by-step explanation: Hope this helps!

Svet_ta [12.7K] · Answer 2 · 2026-02-16T14:50:09+03:00

Answer:

The three errors are:

1) Incorrectly swapping the variables x and y.

2) Failure to use the ± symbol.

3) The domain is wrong; it should be x ≤ 0.

Step-by-step explanation:

Review the following steps.

$y = x^2 + 12x$

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

The initial step is incorrect because the variables x and y were switched improperly; it should be:

$x=y^2+12y$

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

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

Step 4: $y=\sqrt{-11x}$ , for x ≥ 0

Step 4 contains an error as the ± sign is required. Additionally, the function's domain is inaccurately stated.

The radicand must be nonnegative, implying that x must satisfy x ≤ 0.