1. **State the problem:** We are given the function $f(x) = 3 - 5x$ and asked to find the value of its inverse function at $-27$, i.e., find $f^{-1}(-27)$. 2. **Recall the formula for the inverse function:** To find $f^{-1}(y)$, we start with $y = f(x)$ and solve for $x$ in terms of $y$. 3. **Write the equation:** $$y = 3 - 5x$$ 4. **Solve for $x$:** $$y = 3 - 5x$$ $$y - 3 = -5x$$ $$\cancel{y - 3} = \cancel{-5x}$$ $$x = \frac{3 - y}{5}$$ 5. **Express the inverse function:** $$f^{-1}(y) = \frac{3 - y}{5}$$ 6. **Evaluate $f^{-1}(-27)$:** $$f^{-1}(-27) = \frac{3 - (-27)}{5} = \frac{3 + 27}{5} = \frac{30}{5} = 6$$ **Final answer:** $$f^{-1}(-27) = 6$$