1. The problem is to find the inverse of the linear function $f(x) = -x + 2$ in slope-intercept form $y = mx + b$. 2. To find the inverse function $f^{-1}(x)$, we start by replacing $f(x)$ with $y$: $$y = -x + 2$$ 3. Next, swap $x$ and $y$ to find the inverse: $$x = -y + 2$$ 4. Solve for $y$: $$x - 2 = -y$$ 5. Multiply both sides by $-1$ to isolate $y$: $$-1 \cdot (x - 2) = -1 \cdot (-y)$$ $$-x + 2 = y$$ 6. Rewrite $y$ as $f^{-1}(x)$: $$f^{-1}(x) = -x + 2$$ 7. The inverse function is $f^{-1}(x) = -x + 2$, which is the same as the original function. This means the function is its own inverse.