For the given functions $f$ and $g$, complete parts (a)-( $h$ ). For parts (a)-(d), also find the domain
$$f(x)=3x+1;g(x)=7x-6$$
(a) Find $(f+g)(x)$
$$(f+g)(x)=10x-5\text{ (Simplify your answer.) }$$
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 $(f-g)(x)$.
$$(f-g)(x)=◻(\text{ Simplify your answer. })$$

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