Answer
$f+g,f-g,fg$: all real numbers; $\frac{f}{g}$: all real numbers except $-2$
Work Step by Step
For all but $\frac{f}{g}$, the domain includes all real numbers. To find the domain of $\frac{f}{g}$, set the denominator equal to $0$.
$f+g=(3x-4)+(x+2)$
$f+g=4x-2$
$(-∞,∞)$
$f-g=(3x-4)-(x+2)$
$f-g=2x-6$
$(-∞,∞)$
$fg=(3x-4)(x+2)$
$fg=3x^2+2x-8$
$(-∞,∞)$
$\frac{f}{g}=\frac{3x-4}{x+2}$
$x\ne-2$
