find the domain of the function.

\f(x) = \frac{2}{x^2 + 1} + \frac{9}{x^2 - 9}\

what is the domain of f?

(type your answer in interval notation.)

Question

find the domain of the function.

\f(x) = \frac{2}{x^2 + 1} + \frac{9}{x^2 - 9}\

what is the domain of f?

(type your answer in interval notation.)

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Domain of Rational Functions" ], "current_concepts": [ "Domain of Rational Functions", "Interval Notation" ] } ## Identify domain restrictions for each term $$ \begin{aligned} &x^2 + 1 e 0 \implies x^2 e -1 \quad (\text{always true for real } x) \ &x^2 - 9 e 0 \implies (x-3)(x+3) e 0 \implies x e 3 \text{ and } x e -3 \end{aligned} $$ ## Combine restrictions and write in interval notation $$ x \in (-\infty, -3) \cup (-3, 3) \cup (3, \infty) $$ What is the domain of f? $(-\infty, -3) \cup (-3, 3) \cup (3, \infty)$ (Type your answer in interval notation.) { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Domain of Rational Functions" ] }

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Question

Explanation:

Identify domain restrictions for each term

Combine restrictions and write in interval notation

Answer: