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The problem asks you to find \( f(g(-5)) \), given the following functions:

\[
f(x) = 2x - 6
\]
\[
g(x) = x^2 + 6x - 5
\]

To solve this, follow these steps:

1. **Evaluate \( g(-5) \)**:
   \[
   g(x) = x^2 + 6x - 5
   \]
   Substitute \( x = -5 \) into the equation:
   \[
   g(-5) = (-5)^2 + 6(-5) - 5 = 25 - 30 - 5 = -10
   \]

2. **Now find \( f(g(-5)) = f(-10) \)**:
   \[
   f(x) = 2x - 6
   \]
   Substitute \( x = -10 \) into the equation:
   \[
   f(-10) = 2(-10) - 6 = -20 - 6 = -26
   \]

Thus, the value of \( f(g(-5)) \) is \( \boxed{-26} \).

Would you like more details on any step, or do you have any further questions?

Here are 5 related questions you might explore:

1. What happens if you change the input of \( g(x) \) to a different number, say \( g(2) \)?
2. How do you find the inverse of a function like \( f(x) = 2x - 6 \)?
3. Can you compose two functions in reverse order, like finding \( g(f(x)) \)?
4. What is the general process for solving composite functions for any input \( x \)?
5. How do you interpret composite functions graphically?

**Tip:** When evaluating composite functions, always start by solving the innermost function first, then substitute that result into the outer function.

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

Learn how to evaluate composite functions by solving for f(g(-5)) given the functions f(x) = 2x - 6 and g(x) = x^2 + 6x - 5. This problem covers key algebraic concepts and is suitable for students in Grades 8-10.

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