https://file.aiquickdraw.com/mathbot/file/1728005621535wws4a1fl.jpg

In the image, the problem asks you to evaluate a function given two expressions: \( f(x) = x + 3 \) and \( g(x) = x^2 - 2 \). The specific task is to find \( (f \circ g)(6) \), which means to evaluate the composite function \( f(g(6)) \).

Let’s solve it step by step:

1. First, find \( g(6) \):
   \[
   g(x) = x^2 - 2
   \]
   Plugging in \( x = 6 \):
   \[
   g(6) = 6^2 - 2 = 36 - 2 = 34
   \]

2. Now, use this result in the function \( f(x) \), where \( x = g(6) = 34 \):
   \[
   f(x) = x + 3
   \]
   Plugging in \( x = 34 \):
   \[
   f(34) = 34 + 3 = 37
   \]

So, \( (f \circ g)(6) = 37 \).

It seems that the answer provided was incorrect (it showed 34 instead of 37).

Would you like further details or clarification?

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Here are 5 related questions to deepen your understanding:

1. How would you evaluate \( (g \circ f)(6) \)?
2. What is the domain of \( f(x) \) and \( g(x) \)?
3. Can you explain the concept of function composition?
4. How would you graph \( f(x) \) and \( g(x) \) together?
5. What happens if we switch the order of the functions in composition?

**Tip:** Always remember to evaluate the inner function first when working with composite functions.

Evaluate the composite function (f ∘ g)(6), where f(x) = x + 3 and g(x) = x^2 - 2.

Learn how to evaluate the composite function (f ∘ g)(6), where f(x) = x + 3 and g(x) = x^2 - 2. Follow a detailed step-by-step process to solve this function composition problem, ideal for students in Grades 8-10.

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