https://file.aiquickdraw.com/mathbot/file/1727146708859up0kc4qt.jpg

The equation in the image appears to represent the composition of two functions and the evaluation of one of them at a specific point. Let's break it down:

The notation \( (f \circ g)(x) \) means the composition of functions \( f \) and \( g \), and it is defined as:

\[
(f \circ g)(x) = f(g(x))
\]

In the image, the equation proceeds as follows:

1. \( (f \circ g)(x) = f(g(x)) \)
2. \( f(g(x)) = f(x^2 - 9) \)

This suggests that the function \( g(x) \) is defined as:

\[
g(x) = x^2 - 9
\]

Thus, the composition of \( f \) and \( g \), evaluated at \( x \), is given by substituting \( g(x) \) into \( f \):

\[
(f \circ g)(x) = f(x^2 - 9)
\]

Do you need help with a specific part of this problem, or would you like further details on function composition or solving this kind of expression?

Here are five related questions that can extend your understanding:

1. How do you find the composition of two arbitrary functions \( f \) and \( g \)?
2. If \( f(x) = 3x + 2 \) and \( g(x) = x^2 - 9 \), what is \( (f \circ g)(x) \)?
3. What are the conditions for two functions to be composed?
4. How can the domain of \( (f \circ g)(x) \) be affected by the domain of \( g(x) \)?
5. How does the composition of functions differ from multiplication of functions?

**Tip:** Always check the domain of both functions when composing them, as the domain of the composition is restricted by the domain of the inner function.

Explore how to solve the composition of functions with f(g(x)) and understand the relationship between the functions f and g. This problem demonstrates function composition using the equation (f°g)(x) = f(x² - 9), suitable for students in Grades 10-12.

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