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{ "quality": "incomplete", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Inverse Functions", "Finding Inverse Functions" ], "current_concepts": [ "Inverse Functions", "Finding Inverse Functions" ] } ## Identify the original function from the options $$ \begin{aligned} &\text{Let } y = f(x) = \frac{x^2}{49} \quad (x \ge 0)\ &\text{Then } f^{-1}(x) = 7\sqrt{x} \end{aligned} $$ ## Swap variables and solve for y $$ \begin{aligned} &x = \frac{y^2}{49} \quad (y \ge 0)\ &y^2 = 49x\ &y = 7\sqrt{x} \end{aligned} $$ ## Match with the given options $$ f^{-1}(x) = 7\sqrt{x} $$

(A) $f^{-1}(x) = 7\sqrt{x}$

(B) $f^{-1}(x) = \frac{1}{7x}$

(C) $f^{-1}(x) = 7x$

(D) $f^{-1}(x) = \frac{\sqrt{x}}{7}$

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

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Question

Explanation:

Identify the original function from the options

Swap variables and solve for y

Match with the given options

Answer: