https://file.aiquickdraw.com/mathbot/file/17334460294622uytu72n.jpg

The visible portion of the uploaded image contains the following functions and task:

### Functions:
- \( f(x) = x^2 + x - 6 \)
- \( g(x) = 2x - 1 \)

### Task:
- **Evaluate \( g(f(5)) \)** (Find the value of \( g(f(5)) \)).

Let's solve it step by step.

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#### Step 1: Find \( f(5) \)
Substitute \( x = 5 \) into \( f(x) = x^2 + x - 6 \):

\[
f(5) = 5^2 + 5 - 6 = 25 + 5 - 6 = 24
\]

So, \( f(5) = 24 \).

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#### Step 2: Find \( g(f(5)) \), which is \( g(24) \)
Substitute \( x = 24 \) into \( g(x) = 2x - 1 \):

\[
g(24) = 2(24) - 1 = 48 - 1 = 47
\]

So, \( g(f(5)) = 47 \).

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### Final Answer:
\[
g(f(5)) = 47
\]

Would you like a detailed explanation of the steps or have any other questions?  

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### Related Questions:
1. How do you evaluate \( g(f(-2)) \) using these functions?
2. What happens if you reverse the operations, finding \( f(g(5)) \)?
3. Can you factor \( f(x) = x^2 + x - 6 \), and what are its roots?
4. What is the domain and range of \( g(x) = 2x - 1 \)?
5. What is the composite function \( g(f(x)) \), and how is it simplified?

### Tip:
Always substitute carefully, step by step, to avoid errors when working with composite functions!

Use the functions f(x) = x^2 + x - 6 and g(x) = 2x - 1 to evaluate g(f(5)).

Learn how to solve the composition of functions g(f(5)) using the given functions f(x) = x^2 + x - 6 and g(x) = 2x - 1. This step-by-step solution covers key algebra concepts such as substitution and function evaluation, suitable for Grades 9-10.

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