Answer
$(f+g)(x)=2x^{2}+x\rightarrow$ $D=(-\infty,+\infty)$
$(f-g)(x)=x \rightarrow$ $D=(-\infty,+\infty)$
$(f.g)(x)=x^{4}+x^{3} \rightarrow$ $D=(-\infty,+\infty)$
$(\frac{f}{g})(x)=\frac{x+1}{x} \rightarrow$ $D=[0,+\infty)$
Work Step by Step
We are given $f(x)=x^{2}+x$ and $g(x)=x^{2}$
$(f+g)(x)=2x^{2}+x\rightarrow$ the domain is $(-\infty,+\infty)$
$(f-g)(x)=x \rightarrow$ the domain is $(-\infty,+\infty)$
$(f.g)(x)=x^{4}+x^{3} \rightarrow$ the domain is $(-\infty,+\infty)$
$(\frac{f}{g})(x)=\frac{x^{2}+x}{x^{2}}=\frac{x+1}{x} \rightarrow$ the domain is $[0,+\infty)$
