To evaluate $(f + g)(3)$ for the functions $f(x) = 3x^2 - 5x + 7$ and $g(x) = x^2 - 4x - 3$, there are two methods. The first method evaluates the combined function $(f + g)(x) = 4x^2 - 9x + 4$ by substituting $x = 3$, yielding $4(3)^2 - 9 \cdot 3 + 4 = 36 - 27 + 4 = 13$. The second method evaluates $f(3)$ and $g(3)$ separately and adds the results. First, find $f(3) = 3(3)^2 - 5(3) + 7 = 27 - 15 + 7 = 19$. Next, find $g(3) = (3)^2 - 4(3) - 3 = 9 - 12 - 3 = -6$. Finally, add the two values: $(f + g)(3) = f(3) + g(3) = 19 + (-6) = 13$. Both methods produce the same result.