https://file.aiquickdraw.com/mathbot/file/17278389108200fw7iz8o.jpg

The expression given in the image is:

\[
(f \circ g)(x) = 5(3x - 1)^3
\]

This represents the composition of two functions, \( f(x) \) and \( g(x) \), such that \( (f \circ g)(x) = f(g(x)) \).

To find \( f(x) \) and \( g(x) \), let's analyze the structure of the composition:

1. The inner function \( g(x) \) should correspond to the part inside the parentheses: \( g(x) = 3x - 1 \).
   
2. The outer function \( f(x) \) should operate on \( g(x) \), which means \( f(x) \) would take an input \( x \) and raise it to the third power, then multiply by 5. Hence, \( f(x) = 5x^3 \).

Thus, we can conclude:
- \( g(x) = 3x - 1 \)
- \( f(x) = 5x^3 \)

Would you like further details or have any questions?

Here are some related questions:
1. How do you verify a composition of functions?
2. Can you find the inverse functions of \( f(x) \) and \( g(x) \)?
3. What happens if the order of composition is reversed, i.e., \( g(f(x)) \)?
4. How would you graph the functions \( f(x) \) and \( g(x) \)?
5. Can you apply the chain rule to differentiate \( (f \circ g)(x) \)?

**Tip:** When working with function compositions, always start by identifying the inner and outer functions.

Learn how to find the functions f(x) and g(x) from the given function composition (f ∘ g)(x) = 5(3x - 1)^3. This problem involves key algebraic concepts of polynomial functions and function composition, suitable for students in Grades 10-12.

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