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)

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)

Accepted Answer

{ "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 to find the inverse relation $$ x = y^2 + 16 $$ ## Solve for y $$ \begin{aligned} x - 16 &= y^2 \ y &= \pm\sqrt{x - 16} \end{aligned} $$

$y = x^2 - 16$

$y = \pm\sqrt{x} - 16$

$y = \pm\sqrt{x - 16}$

$y = x^2 - 4$

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

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Swap variables to find the inverse relation

Solve for y

Answer: