1. **Problem:** Perform the indicated operation for the first problem. Given functions: $$g(n) = n^2 - 3$$ $$h(n) = 2n - 3$$ Expression to verify: $$n^2 - 2n$$ 2. **Formula and rules:** For subtraction of functions, $$(g - h)(n) = g(n) - h(n)$$ Subtract the expressions by distributing the minus sign carefully. 3. **Intermediate work:** $$(g - h)(n) = (n^2 - 3) - (2n - 3)$$ $$= n^2 - 3 - 2n + 3$$ $$= n^2 - 2n + (-3 + 3)$$ $$= n^2 - 2n + 0$$ $$= n^2 - 2n$$ 4. **Explanation:** We subtract each term of $h(n)$ from $g(n)$. The $-3$ and $+3$ cancel out, leaving $n^2 - 2n$. 5. **Final answer:** $$(g - h)(n) = n^2 - 2n$$