1. **State the problem:** We are given two functions $f(x) = x - 5$ and $g(x) = \frac{1}{x} - 1$. We need to find the composition $fg(x)$, which means $f(g(x))$. 2. **Recall the composition formula:** The composition $fg(x)$ means we substitute $g(x)$ into $f$. So, $$fg(x) = f(g(x)) = f\left(\frac{1}{x} - 1\right)$$ 3. **Apply the function $f$ to $g(x)$:** Since $f(x) = x - 5$, replace $x$ by $g(x)$: $$f\left(\frac{1}{x} - 1\right) = \left(\frac{1}{x} - 1\right) - 5$$ 4. **Simplify the expression:** $$\left(\frac{1}{x} - 1\right) - 5 = \frac{1}{x} - 1 - 5 = \frac{1}{x} - 6$$ 5. **Final answer:** $$fg(x) = \frac{1}{x} - 6$$ This means the composition $fg(x)$ takes an input $x$, applies $g$ first, then applies $f$ to the result, yielding $\frac{1}{x} - 6$.