1. **Problem Statement:** Verify if the functions $f(x) = \frac{1}{2}x - 7$ and $g(x) = 2x - 14$ are inverse functions by using composition of functions. 2. **Formula and Rule:** Two functions $f$ and $g$ are inverses if and only if $f(g(x)) = x$ and $g(f(x)) = x$ for all $x$ in the domains. 3. **Calculate $f(g(x))$:** $$f(g(x)) = f\left(2x - 14\right) = \frac{1}{2}(2x - 14) - 7 = x - 7 - 7 = x - 14$$ 4. **Calculate $g(f(x))$:** $$g(f(x)) = g\left(\frac{1}{2}x - 7\right) = 2\left(\frac{1}{2}x - 7\right) - 14 = x - 14 - 14 = x - 28$$ 5. **Interpretation:** Since $f(g(x)) = x - 14 \neq x$ and $g(f(x)) = x - 28 \neq x$, the compositions do not return the input $x$. 6. **Conclusion:** Therefore, $f$ and $g$ are not inverse functions because their compositions do not simplify to the identity function $x$.