1. **State the problem:** We need to find the value of the function $g(x) = -4x + 7$ when $x = -1$. 2. **Formula used:** The function is given by $g(x) = -4x + 7$. 3. **Substitute the value:** Replace $x$ with $-1$ in the function: $$g(-1) = -4(-1) + 7$$ 4. **Simplify:** Multiply $-4$ by $-1$: $$g(-1) = 4 + 7$$ 5. **Add:** $$g(-1) = 11$$ **Final answer:** $g(-1) = 11$.