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Find \( g(0), g(-4), g(7) \), and \( g\left(\frac{3}{2}\right) \operatorname{lor} g(x)=\frac{x}{\sqrt{16-x^{2}}} \) Find \( g(0) \) Select the correct choice below and if nocessary, fill in the answor box to complete your choice A. \( g(0)=0 \) (Simplify your answer. Type an exacl onswer, using radicals as needed) B. \( \mathbf{g}(0) \) does not exist. C. \( g(0) \) is not a real number. Find \( g(-4) \). Select the correct choice bolow and, if necassary, fill in the answer box to complete your choice. A. \( 9(-4)= \) \( \square \) (Simplify your answer. Type an exact answer, using radicals as needed ) B. \( g(-4) \) does not exist. C. \( g(-4) \) is not a real number.

Ask by Hart Summers. in the United States
Jan 22,2025

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\( g(0) = 0 \) \( g(-4) \) does not exist.

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To find \( g(0) \), we substitute \( x = 0 \) into the function \( g(x) = \frac{x}{\sqrt{16 - x^2}} \): \[ g(0) = \frac{0}{\sqrt{16 - 0^2}} = \frac{0}{\sqrt{16}} = 0 \] So, the correct choice is: A. \( g(0) = 0 \) Next, let's find \( g(-4) \). Substituting \( x = -4 \) into the function: \[ g(-4) = \frac{-4}{\sqrt{16 - (-4)^2}} = \frac{-4}{\sqrt{16 - 16}} = \frac{-4}{\sqrt{0}} \] Since you cannot divide by zero, \( g(-4) \) does not exist. Thus, the correct choice is: B. \( g(-4) \) does not exist.

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