1. **State the problem:** We are given two functions $f(x) = x - 7$ and $g(x) = x^2 - 2x + 3$. We need to find the expression for the composition $g(f(x))$. 2. **Recall the composition formula:** The composition $g(f(x))$ means we substitute $f(x)$ into $g(x)$ wherever we see $x$. So, $$g(f(x)) = g(x - 7) = (x - 7)^2 - 2(x - 7) + 3$$ 3. **Expand and simplify:** $$ (x - 7)^2 = x^2 - 2 \cdot 7 \cdot x + 7^2 = x^2 - 14x + 49 $$ $$ -2(x - 7) = -2x + 14 $$ Putting it all together: $$ g(f(x)) = x^2 - 14x + 49 - 2x + 14 + 3 $$ 4. **Combine like terms:** $$ g(f(x)) = x^2 - 14x - 2x + 49 + 14 + 3 = x^2 - 16x + 66 $$ 5. **Final answer:** The expression representing $g(f(x))$ is $$\boxed{x^2 - 16x + 66}$$ This corresponds to answer choice B.