#### Sum and Product of Functions

- Different functions can be added or multiplied together.

- Say there is two functions f(x) and g(x). We write their sum as (f+g)(x), and product as (fg)(x). In particular, f+g is the sum, fg is the product.

- Thus, to be clearer, it simply means

\begin{aligned} (f+g)(x) &=f(x)+g(x) \\(f g)(x) &=f(x) g(x)\end{aligned}

- When performing such functions, we have to be aware of the domain. For the sum and product to be defined, the domain of this combined function must be in both the domain of f and g.