Describe the steps involved in finding the inverse of a function algebraically.

To find the inverse of a function algebraically, follow these steps: 1. **Verify Invertibility:** Ensure the function is one-to-one and onto. 2. **Replace \( f(x) \) with \( y \):** Write \( y = f(x) \). 3. **Swap \( x \) and \( y \):** Change the equation to \( x = f(y) \). 4. **Solve for \( y \):** Isolate \( y \) in terms of \( x \). 5. **Express the Inverse:** Write \( f^{-1}(x) = y \). 6. **Verify the Inverse:** Check that \( f(f^{-1}(x)) = x \) and \( f^{-1}(f(x)) = x \). By following these steps, you can algebraically determine the inverse of a function.