if $f(x) = \sqrt{x-3}$, which inequality can be used to find the domain of $f(x)$?

* $\sqrt{x-3} \ge 0$
* $x-3 \ge 0$
* $\sqrt{x-3} \le 0$
* $x-3 \le 0$

Question

if $f(x) = \sqrt{x-3}$, which inequality can be used to find the domain of $f(x)$?

* $\sqrt{x-3} \ge 0$
* $x-3 \ge 0$
* $\sqrt{x-3} \le 0$
* $x-3 \le 0$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Domain of Square Root Functions" ], "new_concepts": [], "current_concepts": [ "Domain of Square Root Functions" ] } ## Identify the condition for a real square root $$ \text{For } \sqrt{g(x)} \text{ to be defined in the real numbers, we must have } g(x) \ge 0 $$ ## Apply the condition to the given function $$ \begin{aligned} &f(x) = \sqrt{x-3} \ &x - 3 \ge 0 \end{aligned} $$

(A) $\sqrt{x-3} \ge 0$

(B) $x-3 \ge 0$

(C) $\sqrt{x-3} \le 0$

(D) $x-3 \le 0$

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

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QUESTION IMAGE

Question

Explanation:

Identify the condition for a real square root

Apply the condition to the given function

Answer: