SOLUTION
Step 1 :
Given
[tex]\begin{gathered} f(x)=x^2\text{ + x } \\ \text{g ( x ) =x }^2 \end{gathered}[/tex][tex]\begin{gathered} 1.(f+g)(x)=x^2+x+x^2=2x^2\text{ + x} \\ (f+g)(x)=2x^2\text{ + x } \end{gathered}[/tex][tex]\begin{gathered} 2.\text{ Domain of ( f + g ) ( x ) = ( -}\infty\text{ , }\infty\text{ )} \\ \end{gathered}[/tex][tex]\begin{gathered} 3.(f-g)(x)=x^2+x-x^2\text{ = x} \\ (\text{ f - g ) (x) = x } \end{gathered}[/tex][tex]4.\text{ Domain of ( f - g ) ( x ) = (- }\infty\text{ , }\infty\text{ )}[/tex][tex]5.fg(x)=(x^2+x)x^2=x^{\text{4 }}+x^3[/tex][tex]6.\text{ Domain of fg ( x ) = ( - }\infty\text{ , }\infty\text{ )}[/tex][tex]7.\text{ (}\frac{f}{g}\text{ )x = }\frac{x^2\text{ + x}}{x^2}\text{ = 1 + }\frac{1}{x}[/tex]