1. **State the problem:** We are given two functions: $$f(x) = -x - 5$$ $$g(x) = 2x^2 - 6x - 3$$ We need to find the value of the composition $f(g(1))$. 2. **Recall the composition of functions:** The composition $f(g(1))$ means we first find $g(1)$, then substitute that result into $f(x)$. 3. **Calculate $g(1)$:** $$g(1) = 2(1)^2 - 6(1) - 3 = 2 - 6 - 3$$ Simplify: $$2 - 6 - 3 = -7$$ 4. **Substitute $g(1) = -7$ into $f(x)$:** $$f(g(1)) = f(-7) = -(-7) - 5$$ Simplify: $$-(-7) - 5 = 7 - 5 = 2$$ 5. **Final answer:** $$f(g(1)) = 2$$