1. **State the problem:** We are given the function $$f(-x) = \frac{4}{(-x)^2 + (-x) + 4}$$ and need to simplify it. 2. **Recall the rules:** - Squaring a negative number: $$(-x)^2 = x^2$$ because squaring removes the negative sign. - Simplify expressions inside the denominator. 3. **Simplify the denominator:** $$(-x)^2 + (-x) + 4 = x^2 - x + 4$$ 4. **Rewrite the function:** $$f(-x) = \frac{4}{x^2 - x + 4}$$ 5. **Final answer:** The simplified form of the function is $$f(-x) = \frac{4}{x^2 - x + 4}$$ This shows how the function behaves when the input is replaced by $$-x$$.