To find the composite function fg(x) where f(x) = 9x² and g(x) = x³, we first need to understand what composite functions are. A composite function means that we take the output of one function and use it as the input for another function.
In this case, fg(x) means we want to calculate f(g(x)). So, we’ll start by determining g(x):
- g(x) = x³
Next, we’ll substitute g(x) into f(x):
- f(g(x)) = f(x³)
Now, we need to find f(x³), where f(x) is 9x²:
- f(x³) = 9(x³)²
Calculating (x³)² gives us x6:
- f(x³) = 9x6
Therefore, the composite function fg(x) is:
- fg(x) = 9x6
In summary, after substituting g(x) into f(x), we have found that:
Final Result:
- fg(x) = 9x6