1. **State the problem:** We are given four functions: $$f(x) = 3x - 7, \quad g(x) = 2x^2 - 3x + 1, \quad h(x) = 4x + 1, \quad k(x) = -x^2 + 3$$ We need to find the function $(k - g)(x)$, which means subtracting $g(x)$ from $k(x)$. 2. **Formula and rules:** The subtraction of two functions $k(x)$ and $g(x)$ is defined as: $$ (k - g)(x) = k(x) - g(x) $$ When subtracting polynomials, subtract each corresponding term. 3. **Calculate $(k - g)(x)$:** $$ (k - g)(x) = (-x^2 + 3) - (2x^2 - 3x + 1) $$ Distribute the minus sign: $$ = -x^2 + 3 - 2x^2 + 3x - 1 $$ 4. **Combine like terms:** $$ = (-x^2 - 2x^2) + 3x + (3 - 1) $$ $$ = -3x^2 + 3x + 2 $$ 5. **Final answer:** $$ (k - g)(x) = -3x^2 + 3x + 2 $$ This matches the third option given.