2. Find the domain of the function. Express your answer in interval notation. \[ g(x)=\frac{x-3}{x+4} \]

To find the domain of the function \( g(x) = \frac{x-3}{x+4} \), we need to determine the values of \( x \) for which the function is defined. The function is a rational function, and it is undefined when the denominator is equal to zero. First, we set the denominator equal to zero and solve for \( x \): \[ x + 4 = 0 \] Subtracting 4 from both sides gives: \[ x = -4 \] This means that the function \( g(x) \) is undefined at \( x = -4 \). Therefore, the domain of \( g(x) \) includes all real numbers except \( -4 \). In interval notation, we express the domain as: \[ (-\infty, -4) \cup (-4, \infty) \] Thus, the domain of the function \( g(x) \) is: \[ \boxed{(-\infty, -4) \cup (-4, \infty)} \]