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It looks like you're working with composite functions based on the image you uploaded. You have the following two expressions involving function composition:

1. \((f \circ g)(x)\)
2. \((g \circ f)(x)\)

To clarify:
- \((f \circ g)(x)\) represents the composition of \(f(x)\) and \(g(x)\), meaning \(f(g(x))\). You apply \(g(x)\) first, then apply \(f\) to the result of \(g(x)\).
- \((g \circ f)(x)\) represents the reverse, \(g(f(x))\). You apply \(f(x)\) first, then apply \(g\) to the result of \(f(x)\).

To solve these, you will need the explicit forms of \(f(x)\) and \(g(x)\). Could you provide those functions? Once we have them, I can help you calculate these compositions.

Do you have any questions or would you like to provide the functions to continue? 

Here are 5 questions to think about:

1. What are the specific definitions of \(f(x)\) and \(g(x)\)?
2. Are \(f(x)\) and \(g(x)\) both polynomials, or do they involve more complex functions?
3. Have you studied function composition in terms of domain restrictions yet?
4. How does composition relate to inverse functions?
5. Can you think of real-life applications where function composition might be useful?

**Tip**: Always check the domain of the inner function (like \(g(x)\) in \(f(g(x))\)) to ensure that its output is valid for the outer function \(f\).

(f ∘ g)(x) and (g ∘ f)(x) expressions for function composition

Explore function composition with the expressions (f ∘ g)(x) = f(g(x)) and (g ∘ f)(x) = g(f(x)). Learn how to apply these formulas and understand their importance in algebra. Suitable for students in Grades 9-12.

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