which function is undefined for $x = 0$?

* $y = \sqrt3{x - 2}$
* $y = \sqrt{x - 2}$
* $y = \sqrt3{x + 2}$
* $y = \sqrt{x + 2}$

Question

which function is undefined for $x = 0$?

* $y = \sqrt3{x - 2}$
* $y = \sqrt{x - 2}$
* $y = \sqrt3{x + 2}$
* $y = \sqrt{x + 2}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Square Root Function Domain", "Cube Root Function Domain" ], "new_concepts": [], "current_concepts": [ "Square Root Function Domain", "Cube Root Function Domain", "Function Evaluation" ] } ## Evaluate the cube root functions at x = 0 Using the *Cube Root Function Domain* knowledge point $$ \begin{aligned} &y = \sqrt[3]{x-2} \implies y(0) = \sqrt[3]{0-2} = \sqrt[3]{-2} \in \mathbb{R}\ &y = \sqrt[3]{x+2} \implies y(0) = \sqrt[3]{0+2} = \sqrt[3]{2} \in \mathbb{R} \end{aligned} $$ ## Evaluate the square root functions at x = 0 Using the *Square Root Function Domain* knowledge point $$ \begin{aligned} &y = \sqrt{x-2} \implies y(0) = \sqrt{0-2} = \sqrt{-2} otin \mathbb{R}\ &y = \sqrt{x+2} \implies y(0) = \sqrt{0+2} = \sqrt{2} \in \mathbb{R} \end{aligned} $$ ## Identify the undefined function The function $y = \sqrt{x-2}$ is undefined for $x = 0$ in the set of real numbers because the radicand is negative.

(A) $y = \sqrt[3]{x-2}$

(B) $y = \sqrt{x-2}$

(C) $y = \sqrt[3]{x+2}$

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

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Square Root Function Domain" ] }

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QUESTION IMAGE

Question

Explanation:

Evaluate the cube root functions at x = 0

Evaluate the square root functions at x = 0

Identify the undefined function

Answer: