Find the domain of the following rational function. g(x)=(-8x^2)/((x-7)(x+2)) Select the correct choice below and, if necessary, fill in the answer A. The domain of g(x) is restricted to square (Type your answer in interval notation. B. The domain of g(x) has no restrictions.

To find the domain of the rational function \( g(x) = \frac{-8x^2}{(x-7)(x+2)} \), we need to determine where the function is undefined. A rational function is undefined wherever its denominator is equal to zero.<br /><br />The denominator of \( g(x) \) is \((x-7)(x+2)\). We set this equal to zero and solve for \( x \):<br /><br />\[<br />(x-7)(x+2) = 0<br />\]<br /><br />This equation is satisfied when either \( x-7 = 0 \) or \( x+2 = 0 \).<br /><br />Solving these equations gives:<br /><br />1. \( x - 7 = 0 \) implies \( x = 7 \)<br />2. \( x + 2 = 0 \) implies \( x = -2 \)<br /><br />Thus, the function \( g(x) \) is undefined at \( x = 7 \) and \( x = -2 \).<br /><br />Therefore, the domain of \( g(x) \) excludes these two values. In interval notation, the domain is:<br /><br />\[<br />(-\infty, -2) \cup (-2, 7) \cup (7, \infty)<br />\]<br /><br />So, the correct choice is:<br /><br />A. The domain of \( g(x) \) is restricted to \( (-\infty, -2) \cup (-2, 7) \cup (7, \infty) \).