\[ \begin{array}{l} f(x)=x-4 \\ g(x)=x^{2}-4 x+7 \end{array} \] Find: $(g \circ f)(x)$

Step 1 ：\(g(f(x)) = (f(x))^2 - 4f(x) + 7\)

Step 2 ：Substitute \(f(x) = x - 4\) into the equation

Step 3 ：\(g(f(x)) = (x - 4)^2 - 4(x - 4) + 7\)

Step 4 ：Expand the equation to get \(g(f(x)) = x^2 - 8x + 16 - 4x + 16 + 7\)

Step 5 ：Simplify the equation to get \(g(f(x)) = x^2 - 12x + 39\)

Step 6 ：\(\boxed{g(f(x)) = x^2 - 12x + 39}\)