When students work on equations with functions, they often make some common mistakes. These mistakes can make it harder for them to understand the topic and do well. Here are some important things to keep in mind:

1. Confusing Function Notation: Students sometimes think that $f(x)$ means to multiply. It’s important to know that $f(x)$ actually shows the value of a function, not a product.

2. Forgetting Domain Restrictions: Not paying attention to the domain of a function can lead to wrong answers. For example, if the function is $g(x) = \frac{1}{x-2}$, students need to remember that $x$ cannot be 2.

3. Making Algebra Mistakes: Many students make simple math errors like mixing up terms or not distributing numbers correctly. These kinds of mistakes happen in over 30% of student work. Being careful is very important, especially when solving equations like $2f(x) + 3 = 11$.

4. Errors in Graphing: Students often misunderstand how to read graphs of functions. Only about half of them can correctly find intercepts or asymptotes, which are key to understanding how a function behaves.

5. Missing Multiple Solutions: When solving equations like $x^2 = 4$, a lot of students forget to include negative solutions. It’s important to recognize all possible answers.

By knowing about these common mistakes, students can improve how they tackle problems with functions.