We have the next two functions:
1.
[tex]f(x)=x-2[/tex]
2.
[tex]g(x)=2x^2[/tex]
(a) We must find (f + g) (x)
To find it we must use that
[tex](f+g)(x)=f(x)+g(x)[/tex]
Now, replacing the functions we obtain
[tex]\begin{gathered} (f+g)(x)=x-2+2x^2 \\ \text{Organizing the terms} \\ (f+g)(x)=2x^2+x-2 \end{gathered}[/tex]
Then, the domain of f + g is
[tex]\text{ The domain is }\mleft\lbrace x\mright|x\text{ is any real number}\}[/tex]
(b) We must find (f - g) (x)
To find it we must use that
[tex](f-g)(x)=f(x)-g(x)[/tex]
Now, replacing the functions we obtain
[tex]\begin{gathered} (f-g)(x)=x-2-2x^2 \\ \text{ Organizing the terms} \\ (f-g)(x)=-2x^2+x-2 \end{gathered}[/tex]
Then, the domain of f - g is
[tex]\text{The domain is }\lbrace x|x\text{ is any real number}\}[/tex]
