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We are tasked with finding \((g \circ f)(4)\), which means evaluating the composition \(g(f(4))\).

Given:
- \(f(x) = x^2 - 3x + 3\)
- \(g(x) = 2x - 1\)

### Step 1: Find \(f(4)\)
Substitute \(x = 4\) into \(f(x)\):
\[
f(4) = 4^2 - 3(4) + 3 = 16 - 12 + 3 = 7
\]

### Step 2: Find \(g(f(4)) = g(7)\)
Now substitute \(x = 7\) into \(g(x)\):
\[
g(7) = 2(7) - 1 = 14 - 1 = 13
\]

### Final Answer:
\[
(g \circ f)(4) = 13
\]

Would you like further explanation or details?

Here are some related questions:
1. What is \((f \circ g)(4)\)?
2. How do you evaluate the composition of two functions in general?
3. Can you find \((g \circ f)(x)\) for any \(x\)?
4. How would this problem change if \(g(x)\) were a different function?
5. What does the composition of functions represent graphically?

**Tip**: Always work step-by-step when evaluating compositions, starting from the inside function!

Given the definitions of f(x) = x^2 - 3x + 3 and g(x) = 2x - 1, find the value of (g ∘ f)(4).

Learn how to find the value of (g ∘ f)(4) where f(x) = x^2 - 3x + 3 and g(x) = 2x - 1. This problem demonstrates the steps to evaluate a function composition by first solving f(4) and then applying g to the result. Suitable for Grades 9-12.

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