To evaluate $(f - g)(-2)$ for the functions $f(x) = 3x^2 - 5x + 7$ and $g(x) = x^2 - 4x - 3$, use the combined difference function $(f - g)(x) = 2x^2 - x + 10$. Substitute $-2$ for $x$ in the expression. Using parentheses for substitution gives $2(-2)^2 - (-2) + 10$. Evaluate the exponent first to get $2(4) - (-2) + 10$. Perform the multiplication and handle the double negative to obtain $8 + 2 + 10$. Add the numbers to find the final value: $(f - g)(-2) = 20$.