which equation is the inverse of (y = x^2 + 16)? * (y = x^2 - 16) * (y = \\pm\\sqrt{x} - 16) * (y = \\pm\\sqrt{x - 16}) * (y = x^2 - 4)

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Inverse Functions" ], "new_concepts": [], "current_concepts": [ "Inverse Functions" ] } ## Swap variables \[ x = y^2 + 16 \] ## Solve for y \[ \begin{aligned} y^2 &= x - 16 \\ y &= \pm\sqrt{x - 16} \end{aligned} \] (A) \(y = x^2 - 16\) (B) \(y = \pm\sqrt{x} - 16\) (C) \(y = \pm\sqrt{x - 16}\) (D) \(y = x^2 - 4\) { "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Inverse Functions" ] }

which equation is the inverse of (y = x^2 + 16)? * (y = x^2 - 16) * (y …

QUESTION IMAGE

Question

which equation is the inverse of (y = x^2 + 16)?

(y = x^2 - 16)
(y = \pm\sqrt{x} - 16)
(y = \pm\sqrt{x - 16})
(y = x^2 - 4)

Explanation:

Response

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"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"multiple_choice_formatter",
"explain_then_answer",
"quick"
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"concepts_used": [
"Inverse Functions"
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"new_concepts": [],
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Swap variables

\[
x = y^2 + 16
\]

Solve for y

\[

\begin{aligned} y^2 &= x - 16 \\ y &= \pm\sqrt{x - 16} \end{aligned}

\]
</reasoning>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Algebra",
"Inverse Functions"
]
}
</post_analysis>

Answer: