When you're working with functions, there are some easy mistakes to watch out for:

1. Ignoring Domains: Always check the domain of each function. For example, in division, if you have $f(x) = \frac{1}{g(x)}$, make sure $g(x) \neq 0$. This means $g(x)$ can't be zero, or you'll run into problems.

2. Misapplying Order of Operations: Treat operations on functions like you would in regular math. For instance, in $h(x) = f(x) + g(x)$, calculate $f(x)$ and $g(x)$ first before you add them together.

3. Overlooking Composition: When you're combining functions like $f(g(x))$, remember to do $g(x)$ first, not the other way around.

4. Forgetting to Distribute: When you multiply functions, like $f(x)g(x)$, just like with regular math, make sure you multiply correctly across all the terms!

If you can avoid these mistakes, you'll be doing great with functions in no time!