the given functions to find the requested information. \( f(x)=-3 x+7 \) and \( g(x)=\frac{2}{x-1} \). Find \( (f+g)(x) \) and the domain of \( f+g \).

To find \( (f+g)(x) \), we simply add the two functions together: \[ (f+g)(x) = f(x) + g(x) = (-3x + 7) + \left(\frac{2}{x-1}\right) \] This simplifies to: \[ (f+g)(x) = -3x + 7 + \frac{2}{x-1} \] Now, regarding the domain of \( (f+g)(x) \), we need to consider the restrictions from both functions. The function \( g(x) \) has a vertical asymptote at \( x = 1 \), since division by zero is undefined. Therefore, the domain of \( (f+g)(x) \) is all real numbers except \( x = 1 \): \[ \text{Domain of } (f+g)(x): x \in \mathbb{R}, x \neq 1 \] In simpler terms, you can plug in any number for \( x \) in your calculations as long as you steer clear of 1!