1. **State the problem:** Given the functions $f(x) = 3x - 7$, $g(x) = 2x^2 - 3x + 1$, $h(x) = 4x + 1$, and $k(x) = -x^2 + 3$, find the value of $f(x) - g(x)(-2)$. 2. **Recall the formula and rules:** To find $f(x) - g(x)(-2)$, we first evaluate $g(-2)$ and then subtract it from $f(x)$. This means: $$f(x) - g(-2)$$ 3. **Evaluate $g(-2)$:** $$g(-2) = 2(-2)^2 - 3(-2) + 1 = 2(4) + 6 + 1 = 8 + 6 + 1 = 15$$ 4. **Substitute $g(-2)$ into the expression:** $$f(x) - g(-2) = (3x - 7) - 15$$ 5. **Simplify the expression:** $$3x - 7 - 15 = 3x - 22$$ 6. **Interpretation:** The expression $f(x) - g(x)(-2)$ simplifies to $3x - 22$. Since the question asks for a value, we need to check if $x$ is given or if the question is about the value of the expression at some $x$. Since no $x$ is specified, the expression is $3x - 22$. 7. **Check multiple choice answers:** The options are numbers (-6, 14, -28, 6), so likely the question expects the value of $f(x) - g(x)(-2)$ at some $x$. Since no $x$ is given, possibly the question means $f(-2) - g(-2)$. 8. **Evaluate $f(-2)$:** $$f(-2) = 3(-2) - 7 = -6 - 7 = -13$$ 9. **Calculate $f(-2) - g(-2)$:** $$-13 - 15 = -28$$ 10. **Final answer:** $-28$ matches one of the multiple choice options. **Answer:** $-28$