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We are asked to find the value of \((g \circ f)(-2)\), which means we need to compute \(g(f(-2))\).

Here are the steps to solve this problem:

1. **Find \(f(-2)\):**
   The function \(f(x)\) is given as:
   \[
   f(x) = -2x + 7
   \]
   Substituting \(-2\) into \(f(x)\):
   \[
   f(-2) = -2(-2) + 7 = 4 + 7 = 11
   \]

2. **Find \(g(f(-2)) = g(11)\):**
   The function \(g(x)\) is given as:
   \[
   g(x) = x^2 - 6x + 5
   \]
   Now substitute \(11\) into \(g(x)\):
   \[
   g(11) = 11^2 - 6(11) + 5 = 121 - 66 + 5 = 60
   \]

Thus, \((g \circ f)(-2) = 60\).

Would you like further details on any of these steps?

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Here are 5 related questions to expand on this:

1. What is the general process for finding the composition of two functions?
2. How can you verify the result of a function composition algebraically?
3. What is the domain of the composed function \((g \circ f)(x)\)?
4. How would the result change if we composed \(f(g(x))\) instead of \(g(f(x))\)?
5. Can the order of composition of functions affect the outcome?

**Tip:** When composing functions, always compute the inner function first and then apply the outer function.

Given the definitions of f(x) and g(x) below, find the value of (g ∘ f)(-2).
f(x) = -2x + 7
g(x) = x^2 - 6x + 5

Learn how to find the value of the composite function (g ∘ f)(-2) using the definitions of f(x) = -2x + 7 and g(x) = x^2 - 6x + 5. This problem involves function composition, algebra, and quadratic equations. Suitable for students in Grades 9-11.

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