what is the domain of the function $ y = \ln\left(\frac{-x+3}{2}\ ight) $? $ x 2 $ $ x 3 $

Question

what is the domain of the function $ y = \ln\left(\frac{-x+3}{2}\ ight) $? $ x < 2 $ $ x > 2 $ $ x < 3 $ $ x > 3 $

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": [ "Domain of Logarithmic Functions" ], "new_concepts": [], "current_concepts": [ "Domain of Logarithmic Functions", "Linear Inequalities" ] } ## Set up the domain inequality Using the *Domain of Logarithmic Functions* knowledge point $$ \frac{-x + 3}{2} > 0 $$ ## Solve the inequality for x Using the *Linear Inequalities* knowledge point $$ \begin{aligned} -x + 3 &> 0 \ -x &> -3 \ x &< 3 \end{aligned} $$

$x < 2$

$x > 2$

$x < 3$

$x > 3$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Domain of Logarithmic Functions" ] }

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Question

Explanation:

Set up the domain inequality

Solve the inequality for x

Answer: