Find \( g(0), g(-1), g(2) \), and \( g\left(\frac{3}{4}\right) \) for \( g(x)=\frac{x}{\sqrt{1-x^{2}}} \). Find \( g(0) \). Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. \( g(0)=\square \) \( \quad \) (Simplify your answer. Type an exact answer, using radicals as needed.) B. \( g(0) \) does not exist. C. \( g(0) \) is not a real number. Find \( g(-1) \) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. \( g(-1)-\square \) (Simplify your answer. Type an exact annswer, using radicals as needed.) B. \( g(-1) \) does not exist. C. \( g(-1) \) is not a real number. Find \( g(2) \) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. \( g(2)=\square \) (Simplify your answer. Type an exact answer, using radicals as needed.) B. \( g(2) \) does not exist. C. \( g(2) \) is not a real number.
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To find \( g(0) \), we substitute \( x = 0 \) into the function: \[ g(0) = \frac{0}{\sqrt{1-0^{2}}} = \frac{0}{\sqrt{1}} = 0 \] So, the correct choice for \( g(0) \) is: A. \( g(0)=0 \) Next, for \( g(-1) \): \[ g(-1) = \frac{-1}{\sqrt{1-(-1)^{2}}} = \frac{-1}{\sqrt{1-1}} = \frac{-1}{\sqrt{0}} \] Since division by zero is undefined, the correct choice for \( g(-1) \) is: B. \( g(-1) \) does not exist. Now, we check \( g(2) \): \[ g(2) = \frac{2}{\sqrt{1-2^{2}}} = \frac{2}{\sqrt{1-4}} = \frac{2}{\sqrt{-3}} \] This expression involves the square root of a negative number which is not a real number, so the correct choice for \( g(2) \) is: C. \( g(2) \) is not a real number. In summary: 1. \( g(0) = 0 \) 2. \( g(-1) \) does not exist. 3. \( g(2) \) is not a real number.
