How do you find the composite function fg for the functions f(x) = x² and g(x) = x² + 7x + 9 at the point x = 1, and what is the result?

To solve the problem, we need to find the composite function fg at x = 1, where f(x) = x² and g(x) = x² + 7x + 9.

Let’s break down the steps:

1. Calculate g(1): Substitute 1 into the function g(x).
2. g(1) = (1)² + 7(1) + 9 = 1 + 7 + 9 = 17.
3. Next, we need to calculate f(g(1)), which is f(17):
4. f(17) = (17)² = 289.

So, we can summarize our findings:

• g(1) = 17
• f(g(1)) = f(17) = 289

Therefore, the value of fg(1) is 289.

If you have any further questions or need clarification on any of the steps, feel free to ask!