To find the domain of the rational function \( g(x) = \frac{-8x^2}{(x-7)(x+3)} \), we need to identify the values of \( x \) that make the denominator equal to zero, as these values are not included in the domain.
Set the denominator equal to zero:
\[ (x-7)(x+3) = 0 \]
This gives us two equations to solve:
- \( x - 7 = 0 \) → \( x = 7 \)
- \( x + 3 = 0 \) → \( x = -3 \)
The values \( x = 7 \) and \( x = -3 \) are the points where the denominator is zero. Thus, these points must be excluded from the domain.
Therefore, the domain of \( g(x) \) can be expressed in interval notation as follows:
\[ (-\infty, -3) \cup (-3, 7) \cup (7, \infty) \]
So the answer is:
A. The domain of g(x) is restricted to \((- \infty, -3) \cup (-3, 7) \cup (7, \infty)\).