For the given functions $f$ and $g$, complete parts (a)-( $h$ ). For parts (a)-(d), also find the domain \[ f(x)=3 x+1 ; g(x)=7 x-6 \] (a) Find $(f+g)(x)$ \[ (f+g)(x)=10 x-5 \text { (Simplify your answer.) } \] What is the domain of $\mathrm{f}+\mathrm{g}$ ? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The domain is $\{x \mid\}$ (Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.) B. The domain is $\{x \mid x$ is any real number $\}$. (b) Find $(f-g)(x)$. \[ (f-g)(x)=\square(\text { Simplify your answer. }) \]

Step 1 ：Given the functions $f(x) = 3x + 1$ and $g(x) = 7x - 6$.

Step 2 ：We are asked to find the difference of the functions $f$ and $g$, which is given by $(f-g)(x) = f(x) - g(x)$.

Step 3 ：Subtracting the expression for $g(x)$ from the expression for $f(x)$, we get $(f-g)(x) = -4x + 7$.

Step 4 ：The domain of a function is the set of all possible input values (x-values) for which the function is defined. Since both $f$ and $g$ are linear functions, they are defined for all real numbers.

Step 5 ：Therefore, the domain of $(f-g)(x)$ is all real numbers.

Step 6 ：\(\boxed{(f-g)(x) = -4x + 7}\) is the difference of the functions $f$ and $g$, and the domain is \(\boxed{\{x \mid x \text{ is any real number}\}}\).