Answer
$f+g,f-g,fg$: all real numbers; $\frac{f}{g}$: all real numbers except $0$
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 $0$.
$f+g=(x-5)+(3x^2)$
$f+g=3x^2+x-5$
$(-∞,∞)$
$f-g=(x-5)-(3x^2)$
$f-g=x-5-3x^2$
$(-∞,∞)$
$fg=(x-5)(3x^2)$
$fg=3x^3-15x^2$
$(-∞,∞)$
$\frac{f}{g}=\frac{x-5}{3x^2}$
$x\ne0$
