Answer
$\Rightarrow (f-g)(x)=2x^2+x+2$
$\Rightarrow (f-g)(2)=12$.
Work Step by Step
The given functions are
$f(x)=3x^2-4x+1$ and $g(x)=x^2-5x-1$
By using the definition of the difference $f-g$.
$\Rightarrow (f-g)(x)=f(x)-g(x)$
Substitute the given functions.
$\Rightarrow (f-g)(x)=3x^2-4x+1-(x^2-5x-1)$
Remove the parentheses and change the sign of each term in the second set of parentheses.
$\Rightarrow (f-g)(x)=3x^2-4x+1-x^2+5x+1$
Add like terms.
$\Rightarrow (f-g)(x)=2x^2+x+2$
Replace $x$ with $2$ in the above function.
$\Rightarrow (f-g)(2)=2(2)^2+(2)+2$
Clear the parentheses.
$\Rightarrow (f-g)(2)=8+2+2$
Add like terms.
$\Rightarrow (f-g)(2)=12$
