given: $g(x) = \sqrt{x-4}$ and $h(x) = 2x-8$

what are the restrictions on the domain of $g \circ h$?

$x \ge$

Question

given: $g(x) = \sqrt{x-4}$ and $h(x) = 2x-8$

what are the restrictions on the domain of $g \circ h$?

$x \ge$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Composite Functions", "Domain of Composite Functions" ], "new_concepts": [], "current_concepts": [ "Composite Functions", "Domain of Composite Functions" ] } ## Define the composite function $$ (g \circ h)(x) = g(h(x)) = \sqrt{(2x - 8) - 4} = \sqrt{2x - 12} $$ ## Determine the domain restriction $$ \begin{aligned} 2x - 12 &\ge 0 \ 2x &\ge 12 \ x &\ge 6 \end{aligned} $$ Given: $g(x) = \sqrt{x-4}$ and $h(x) = 2x-8$. What are the restrictions on the domain of $g \circ h$? $x \ge$ 6 { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Domain of Composite Functions" ] }

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Question

Explanation:

Define the composite function

Determine the domain restriction

Answer: