1. **State the problem:** Find the difference function $(f - g)(x)$ where $f(x) = 4x + \sqrt{7} - x$ and $g(x) = x^2 - x + 1$. 2. **Write the formula:** $$(f - g)(x) = f(x) - g(x)$$ 3. **Substitute the given functions:** $$(f - g)(x) = (4x + \sqrt{7} - x) - (x^2 - x + 1)$$ 4. **Simplify inside the parentheses:** $$(f - g)(x) = 4x + \sqrt{7} - x - x^2 + x - 1$$ 5. **Combine like terms:** $$4x - x + x = 4x$$ So, $$(f - g)(x) = -x^2 + 4x + \sqrt{7} - 1$$ 6. **Final simplified difference function:** $$(f - g)(x) = -x^2 + 4x + \sqrt{7} - 1$$ --- 1. **Evaluate $(f - g)(-2)$:** Substitute $x = -2$ into the difference function: $$(f - g)(-2) = -(-2)^2 + 4(-2) + \sqrt{7} - 1$$ 2. **Calculate powers and products:** $$-(-2)^2 = -4$$ $$4 \times (-2) = -8$$ 3. **Sum all terms:** $$(f - g)(-2) = -4 - 8 + \sqrt{7} - 1 = -13 + \sqrt{7}$$ 4. **Approximate $\sqrt{7} \approx 2.64575$:** $$(f - g)(-2) \approx -13 + 2.64575 = -10.35425$$ --- 1. **Domain of $(f - g)(x)$:** Since $f(x)$ and $g(x)$ are defined for all real numbers (polynomial and square root of constant), the domain is all real numbers. **Answer:** A. $(-\infty, \infty)$