When students work on inverse functions, they often make some common mistakes. Here are a few to watch out for:

1. Not Switching Variables: A really important step is to switch $x$ and $y$. If you forget to do this, your inverse will be wrong.

2. Misunderstanding the Domain: Sometimes, students don’t check if the original function is one-to-one. If it’s not, the inverse won’t work properly.

3. Algebra Errors: When solving for $y$, the math can be tricky. Even a small mistake can lead to a totally wrong inverse.

4. Ignoring Restrictions: Students might forget to consider the limits on the domain of the inverse function.

Taking your time and looking over each step can help you avoid these mistakes!