Answer
$f+g =2x+3$, domain $\{x|x=all\ real\ numbers \}$
$f-g =1-4x$, domain $\{x|x=all\ real\ numbers \}$
$f\cdot g =2+5x-3x^2$, domain $\{x|x=all\ real\ numbers \}$
$\frac{f}{g}=\frac{2-x}{3x+1}$, domain $\{x|x\ne -\frac{1}{3} \}$
Work Step by Step
Step 1. Given $f(x)=2-x, g(x)=3x+1$, we have $f+g=(2-x)+(3x+1)=2x+3$, domain $\{x|x=all\ real\ numbers \}$
Step 2. We have $f-g=(2-x)-(3x+1)=1-4x$, domain $\{x|x=all\ real\ numbers \}$
Step 3. We have $f\cdot g=(2-x)(3x+1)=2+5x-3x^2$, domain $\{x|x=all\ real\ numbers \}$
Step 4. We have $\frac{f}{g}=\frac{2-x}{3x+1}$, domain $\{x|x\ne -\frac{1}{3} \}$
