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.

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UpStudy AI · Accepted Answer

Let's evaluate the function $$ g(x) = \frac{x}{\sqrt{16 - x^{2}}} $$ at the specified points.

### 1. Find $$ g(0) $$

**Calculation:**
$$
g(0) = \frac{0}{\sqrt{16 - (0)^2}} = \frac{0}{\sqrt{16}} = \frac{0}{4} = 0
$$

**Correct Choice:**
**A.** $$ g(0) = 0 $$

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### 2. Find $$ g(-4) $$

**Calculation:**
$$
g(-4) = \frac{-4}{\sqrt{16 - (-4)^2}} = \frac{-4}{\sqrt{16 - 16}} = \frac{-4}{\sqrt{0}} 
$$
Here, the denominator becomes $$ \sqrt{0} = 0 $$, which leads to division by zero. Division by zero is undefined in the real number system.

**Correct Choice:**
**B.** $$ g(-4) $$ does not exist.

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If you need evaluations for $$ g(7) $$ and $$ g\left(\frac{3}{2}\right) $$, feel free to ask!
$$ g(0) = 0 $$ $$ g(-4) $$ does not exist.

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