To realize the operation, we are going to follow the next development
[tex]\begin{gathered} g(x)-f(x)=(x^2-x+1)-(3x+2) \\ g(x)-f(x)=x^2-x+1-3x-2=x^2-4x-1 \end{gathered}[/tex]
So, the answer to the operation is x^{2}-4x-1. As we have a polynomial function, the domain is given by all real numbers.
