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The problem asks to evaluate \((f \circ g)(3)\), which is the composition of the two functions \(f(x)\) and \(g(x)\), without finding an explicit equation for the composition.

Given:
- \( f(x) = 5x - 3 \)
- \( g(x) = 2x - 7 \)

We need to follow these steps:

1. First, evaluate \(g(3)\) by substituting \(x = 3\) into the equation for \(g(x)\):
   \[
   g(3) = 2(3) - 7 = 6 - 7 = -1
   \]

2. Next, use the result \(g(3) = -1\) as the input for the function \(f(x)\). So now, we evaluate \(f(-1)\):
   \[
   f(-1) = 5(-1) - 3 = -5 - 3 = -8
   \]

Therefore, \((f \circ g)(3) = -8\).

Let me know if you'd like more details or have further questions.

Here are 5 related questions for practice:
1. What is \((g \circ f)(3)\) using the same functions?
2. What is \(g(f(2))\) with the same given functions?
3. How do you find the inverse of \(f(x) = 5x - 3\)?
4. How do you determine if \(f \circ g\) is a one-to-one function?
5. Can you describe the steps to graph the composition \(f(g(x))\)?

**Tip:** When working with function compositions, always evaluate the inner function first, then substitute its output into the outer function.

Let the functions f(x) = 5x - 3 and g(x) = 2x - 7 be given. Evaluate (f ∘ g)(3).

Learn how to evaluate the function composition (f ∘ g)(3) for the functions f(x) = 5x - 3 and g(x) = 2x - 7. This example walks through key steps for solving function compositions and is suitable for students in Grades 9-12.

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