which equation is the inverse of (y = x^2 - 36)?

(y = pmsqrt{x} + 6)
(y = pmsqrt{x + 36})
(y = pmsqrt{x} + 36)
(y = pmsqrt{x^2 + 36})

Question

which equation is the inverse of (y = x^2 - 36)?

(y = pmsqrt{x} + 6)
(y = pmsqrt{x + 36})
(y = pmsqrt{x} + 36)
(y = pmsqrt{x^2 + 36})

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Finding Inverses Algebraically" ], "new_concepts": [], "current_concepts": [ "Inverse Functions", "Finding Inverses Algebraically" ] } ## Swap the variables $x$ and $y$ $$ x = y^2 - 36 $$ ## Solve for $y$ $$ \begin{aligned} x + 36 &= y^2 \ y &= \pm\sqrt{x + 36} \end{aligned} $$

(A) $y = \pm\sqrt{x} + 6$

(B) $y = \pm\sqrt{x + 36}$

(C) $y = \pm\sqrt{x} + 36$

(D) $y = \pm\sqrt{x^2 + 36}$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Finding Inverses Algebraically" ] }

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Question

Explanation:

Swap the variables \(x\) and \(y\)

Solve for \(y\)

Answer: