1. The problem is to find the inverse of a function, which means finding a function that "undoes" the original function. 2. The general formula for finding the inverse of a function $y=f(x)$ is to swap $x$ and $y$ and then solve for $y$. 3. Important rule: The inverse function exists only if the original function is one-to-one (passes the horizontal line test). 4. Suppose the function is $y=f(x)$. To find the inverse: $$x = f(y)$$ Then solve this equation for $y$. 5. Example: If $f(x) = 2x + 3$, then to find $f^{-1}(x)$: $$x = 2y + 3$$ 6. Subtract 3 from both sides: $$x - 3 = 2y$$ 7. Divide both sides by 2: $$\frac{x - 3}{2} = y$$ 8. Using the cancel notation: $$\frac{\cancel{x - 3}}{\cancel{2}} = y$$ 9. So the inverse function is: $$f^{-1}(x) = \frac{x - 3}{2}$$ This means if you input $x$ into $f^{-1}$, you get the original input to $f$ before it was transformed. Final answer: The inverse function is $f^{-1}(x) = \frac{x - 3}{2}$.