f(x) = x − 3, g(x) = x 2
--------------------------------------------
$$f+g=x-3+x^2 \\\\
f+g=x^2+x-3 \mbox{ where x can be any real number - that is }x\in R$$
-------------------------------------------
$$f-g=x-3-x^2 \\\\
f-g=-x^2+x-3 \mbox{ where x can be any real number - that is }x\in R$$
-------------------------------------------------
f(x) = x − 3, g(x) = x 2
$$fg=(x-3)x^2 \\\\
fg=x^3-3x^2 \mbox{ where x can be any real number - that is }x\in R$$
-----------------------------------------------------
$$f/g=(x-3)/x^2 \\\\
\mbox{x cannot be 0 because you can't divide by 0 so }\\\\\mbox{domain: }x\in R \mbox{ where }x\ne 0$$
---------------------------------------------------------
To be honest here I do not see why x cannot be an imaginary number but you probably haven't learned about those yet so these are probably the answers that you need.