1. **State the problem:** Find the inverse of the function $f(x) = 2x + 16$. 2. **Recall the formula and rule:** To find the inverse function $f^{-1}(x)$, we swap $x$ and $y$ in the equation and solve for $y$. The original function is $y = 2x + 16$. 3. **Swap variables:** Replace $f(x)$ with $y$ and swap $x$ and $y$: $$x = 2y + 16$$ 4. **Solve for $y$:** $$x - 16 = 2y$$ Show the cancellation step: $$\cancel{2}y = \frac{x - 16}{\cancel{2}}$$ 5. **Isolate $y$:** $$y = \frac{x - 16}{2}$$ 6. **Write the inverse function:** $$f^{-1}(x) = \frac{x - 16}{2}$$ This means the inverse function takes an input $x$, subtracts 16, then divides by 2 to get the output.