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We are asked to find \( (f \circ g)(-6) \), which is the composition of the functions \( f(x) \) and \( g(x) \).

Given:
- \( f(x) = 2x + 1 \)
- \( g(x) = 3x - 5 \)

The composition \( (f \circ g)(x) \) means applying \( g(x) \) first, then applying \( f \) to the result of \( g(x) \). So we need to compute \( f(g(-6)) \).

### Step-by-step solution:

1. First, calculate \( g(-6) \):
   \[
   g(-6) = 3(-6) - 5 = -18 - 5 = -23
   \]

2. Now, compute \( f(g(-6)) = f(-23) \):
   \[
   f(-23) = 2(-23) + 1 = -46 + 1 = -45
   \]

Thus, \( (f \circ g)(-6) = -45 \).

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Do you want more details or have any questions about this?

Here are some related questions to further explore:
1. What is \( (g \circ f)(x) \) and how is it different from \( (f \circ g)(x) \)?
2. How would you solve \( (f \circ f)(x) \) with the given \( f(x) = 2x + 1 \)?
3. Can you find the inverse of \( f(x) \) or \( g(x) \)?
4. How does the order of composition affect the outcome when combining functions?
5. How would the result change if we evaluated \( (g \circ f)(-6) \)?

**Tip:** Always apply the inner function first when dealing with compositions of functions.

(f°g)(-6), where f(x) = 2x + 1 and g(x) = 3x - 5

Learn how to solve the function composition problem (f°g)(-6) with detailed steps. This example explores linear functions and substitution using f(x) = 2x + 1 and g(x) = 3x - 5, ideal for Grades 9-12.

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