State the domain of the function f(x) = \dfrac{2x}{\sqrt{4-x^2}} .

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BlackTom AI · Accepted Answer

We begin by restating the problem: find the domain of f(x) = 2x / sqrt(4 - x^2). Key principle: the square root in the denominator requires its radicand to be strictly positive (to avoid division by zero and to keep the square root defined over the reals). Therefore, 4 - x^2 must be > 0. Solve the inequality: 4 - x^2 > 0 implies x^2 < 4. This means -2 < x < 2. Thus, the domain consists of all real x strictly between -2 and 2. Note on the provided options: the list of answer options is empty in this item, so there are no alternative statements to evaluate individually. The derived domain, -2 < x < 2, is the correct set of x for which the function is defined. The given answer string '-2 < x < 2' aligns with the correct domain, confirming consistency with the analysis.

FNDN Mathematics for Commerce 2025 STD O1

State the domain of the function f(x) = \dfrac{2x}{\sqrt{4-x^2}} .

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