choose the inverse of $y = x^2 - 10x$.

$y = \pm\sqrt{x - 25} - 5$

$y = \pm\sqrt{x - 25} + 5$

$y = \pm\sqrt{x + 25} - 5$

$y = \pm\sqrt{x + 25} + 5$

Question

choose the inverse of $y = x^2 - 10x$.

$y = \pm\sqrt{x - 25} - 5$

$y = \pm\sqrt{x - 25} + 5$

$y = \pm\sqrt{x + 25} - 5$

$y = \pm\sqrt{x + 25} + 5$

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", "Completing the Square" ], "new_concepts": [], "current_concepts": [ "Finding Inverses Algebraically", "Completing the Square" ] } ## Swap variables to set up the inverse relation $$ x = y^2 - 10y $$ ## Complete the square for the quadratic expression in terms of y $$ \begin{aligned} x + 25 &= y^2 - 10y + 25 \ x + 25 &= (y - 5)^2 \end{aligned} $$ ## Solve for y using the square root property $$ \begin{aligned} y - 5 &= \pm\sqrt{x + 25} \ y &= \pm\sqrt{x + 25} + 5 \end{aligned} $$

(A) $y = \pm\sqrt{x - 25} - 5$

(B) $y = \pm\sqrt{x - 25} + 5$

(C) $y = \pm\sqrt{x + 25} - 5$

(D) $y = \pm\sqrt{x + 25} + 5$

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

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Swap variables to set up the inverse relation

Complete the square for the quadratic expression in terms of y

Solve for y using the square root property

Answer: