1. **State the problem:** We are given two functions $f(x) = \frac{1}{x - 5}$ and $g(x) = 3x + 9$. We need to find the value of $(f \circ g)(7)$ and the expression for $(f \circ g)(x)$. 2. **Recall the composition of functions:** The composition $(f \circ g)(x)$ means $f(g(x))$, which is the function $f$ evaluated at $g(x)$. 3. **Find $(f \circ g)(7)$:** First, find $g(7)$: $$g(7) = 3(7) + 9 = 21 + 9 = 30$$ Now, evaluate $f$ at $g(7) = 30$: $$f(30) = \frac{1}{30 - 5} = \frac{1}{25}$$ So, $(f \circ g)(7) = \frac{1}{25}$. 4. **Find $(f \circ g)(x)$:** Substitute $g(x)$ into $f$: $$ (f \circ g)(x) = f(g(x)) = \frac{1}{g(x) - 5} = \frac{1}{3x + 9 - 5} = \frac{1}{3x + 4} $$ 5. **Final answers:** $$(f \circ g)(7) = \frac{1}{25}$$ $$(f \circ g)(x) = \frac{1}{3x + 4}$$