Composite Functions: f(g(x)) and g(f(x))

The problems in this lesson cover composite functions (also called composition of functions), which are normally written as f(g(x)) and g(f(x)). For example, if f(x) = 3x - 2 and g(x) = root x, find f(g(9)). In this situation, we first find g(9). Since g(x) = root x, then g(9) = root 9, or 3. Therefore, f(g(9)) is the same thing as f(3). And since f(x) = 3x - 2, then f(3) = 3(3) - 2, or 9 -2, which is 7. So f(g(9)) = 7. A common mistake when working with composite functions is to find g(f(x)) when you're supposed to be finding f(g(x)), and vice versa. No composite functions calculator is required, and a self-test serves as an interactive composite functions worksheet.