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Which diagram represents the domain of the function $f(x) = ext{sin}^{-1} \left( \frac{3}{x} \right)$? A - HSC - SSCE Mathematics Extension 1 - Question 7 - 2017 - Paper 1

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Which-diagram-represents-the-domain-of-the-function-$f(x)-=--ext{sin}^{-1}-\left(-\frac{3}{x}-\right)$?--A-HSC-SSCE Mathematics Extension 1-Question 7-2017-Paper 1.png

Which diagram represents the domain of the function $f(x) = ext{sin}^{-1} \left( \frac{3}{x} \right)$? A. B. C. D.

Worked Solution & Example Answer:Which diagram represents the domain of the function $f(x) = ext{sin}^{-1} \left( \frac{3}{x} \right)$? A - HSC - SSCE Mathematics Extension 1 - Question 7 - 2017 - Paper 1

Step 1

Identify the correct diagram

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Answer

Since the domain derived gives intervals that are exclusive of 00, the correct representation of the domain would be the diagram that indicates open intervals for (−3,0)(-3, 0) and (3,∞)(3, \infty). Therefore, the correct option is A, as it shows these segments without including the endpoints.

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