which equation is the inverse of $5y + 4 = (x + 3)^2 + \frac{1}{2}$?

$\bigcirc\ y = \frac{1}{5}x^2 + \frac{6}{5}x + \frac{11}{10}$

$\bigcirc\ y = 3 \pm \sqrt{5x + \frac{7}{2}}$

$\bigcirc\ -5y - 4 = -(x + 3)^2 - \frac{1}{2}$

$\bigcirc\ y = -3 \pm \sqrt{5x + \frac{7}{2}}$

Question

which equation is the inverse of $5y + 4 = (x + 3)^2 + \frac{1}{2}$?

$\bigcirc\ y = \frac{1}{5}x^2 + \frac{6}{5}x + \frac{11}{10}$

$\bigcirc\ y = 3 \pm \sqrt{5x + \frac{7}{2}}$

$\bigcirc\ -5y - 4 = -(x + 3)^2 - \frac{1}{2}$

$\bigcirc\ y = -3 \pm \sqrt{5x + \frac{7}{2}}$

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": [ "Finding Inverses Algebraically", "Inverse Functions" ] } ## Swap variables $x$ and $y$ $$ 5x + 4 = (y + 3)^2 + \frac{1}{2} $$ ## Isolate the squared term $$ \begin{aligned} 5x + 4 - \frac{1}{2} &= (y + 3)^2 \ 5x + \frac{7}{2} &= (y + 3)^2 \end{aligned} $$ ## Solve for $y$ $$ \begin{aligned} y + 3 &= \pm\sqrt{5x + \frac{7}{2}} \ y &= -3 \pm\sqrt{5x + \frac{7}{2}} \end{aligned} $$

(A) $y = \frac{1}{5}x^2 + \frac{6}{5}x + \frac{11}{10}$

(B) $y = 3 \pm \sqrt{5x + \frac{7}{2}}$

(C) $-5y - 4 = -(x + 3)^2 - \frac{1}{2}$

(D) $y = -3 \pm \sqrt{5x + \frac{7}{2}}$

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

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QUESTION IMAGE

Question

Explanation:

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

Isolate the squared term

Solve for \(y\)

Answer: