find the inverse of the function.
$y = x^2 + 4x + 4$

$y = \sqrt{\frac{1}{2}x + 2}$

$y = \pm\sqrt{\frac{1}{2}x + 2}$

$y = \pm\sqrt{x} - 2$

$y = \sqrt{x} - 2$

Question

find the inverse of the function.
$y = x^2 + 4x + 4$

$y = \sqrt{\frac{1}{2}x + 2}$

$y = \pm\sqrt{\frac{1}{2}x + 2}$

$y = \pm\sqrt{x} - 2$

$y = \sqrt{x} - 2$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Inverse Functions" ], "new_concepts": [ "Quadratic Inverse" ], "current_concepts": [ "Inverse Functions", "Quadratic Inverse" ] } ## Swap variables Using the *Inverse Functions* knowledge point $$ x = y^2 + 4y + 4 $$ ## Factor the quadratic expression Using the *Inverse Functions* knowledge point $$ x = (y + 2)^2 $$ ## Solve for y Using the *Inverse Functions* knowledge point $$ \begin{aligned} \pm\sqrt{x} &= y + 2 \ y &= \pm\sqrt{x} - 2 \end{aligned} $$

(A) $y = \sqrt{\frac{1}{2}x + 2}$

(B) $y = \pm\sqrt{\frac{1}{2}x + 2}$

(C) $y = \pm\sqrt{x} - 2$

(D) $y = \sqrt{x} - 2$

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

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Explanation:

Swap variables

Factor the quadratic expression

Solve for y

Answer: