1. **State the problem:** We are given two functions: $$q(x) = \frac{1}{x - 8}$$ $$r(x) = |6x + 7|$$ We need to find the composition $(q \circ r)(x) = q(r(x))$. 2. **Recall the composition formula:** For two functions $f$ and $g$, the composition $(f \circ g)(x) = f(g(x))$. 3. **Apply the formula:** Substitute $r(x)$ into $q(x)$: $$(q \circ r)(x) = q(r(x)) = \frac{1}{r(x) - 8}$$ 4. **Substitute $r(x) = |6x + 7|$:** $$(q \circ r)(x) = \frac{1}{|6x + 7| - 8}$$ 5. **Final answer:** $$(q \circ r)(x) = \frac{1}{|6x + 7| - 8}$$ This expression is defined for all $x$ such that $|6x + 7| - 8 \neq 0$, i.e., $|6x + 7| \neq 8$.