Answer :
[tex]g(x)=x^2+2x-3[/tex]
Here, we want to get the value of g(x)
We can make straight substitution here
[tex]\begin{gathered} \text{From the question;} \\ f(x)-g(x)=2x^2-4x+4 \\ g(x)=f(x)-(2x^2-4x+4) \\ g(x)=(3x^2-2x+1)-(2x^2-4x+4) \\ g(x)=3x^2-2x+1-2x^2+4x-4 \\ g(x)=3x^2-2x^2-2x+4x+1-4 \\ g(x)=x^2+2x-3 \end{gathered}[/tex]