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The image provided contains a problem involving function machines, where the user must determine inputs and outputs based on specific rules. Here's a transcription of the problem for easier reference:

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**Problem:**

Amaliza is working with function machines. She has two machines shown at the link. She wants to put them in order so the output of the first machine becomes the input of the second. Her initial input is 6.

**Questions:**

a. In what order must she put the machines to get a final output of 45?

b. Is it possible for her to find an initial input that will get a final output of 5? If so, show how she could do it. If not, explain why not.

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To solve this, we need to know what the two machines do. Assuming that we are missing the exact functions of the machines, could you share more details on the nature of these machines, or would you prefer a general strategy for solving function-based problems? Let me know if you have more information!

Would you like a detailed explanation on how to approach such problems, or do you have more details on the machines?

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Here are 5 related questions:

1. What are function machines and how are they commonly used in mathematics?
2. How do function compositions work when combining two functions?
3. What are inverse functions, and how do they relate to function machines?
4. How can you determine the order of function machines to achieve a specific output?
5. What methods can be used to find an input if a specific output is desired from function machines?

**Tip**: When dealing with function machines, always keep track of the order of operations, as it can significantly affect the result!

Amaliza is working with function machines. She has two machines and wants to put them in order so that the output of the first machine becomes the input of the second. Her initial input is 6. In what order must she put the machines to get a final output of 45? Is it possible for her to find an initial input that will get a final output of 5? If so, show how she could do it. If not, explain why not.

Explore how to solve a problem involving two function machines with an initial input of 6. Learn how to arrange the machines to get a final output of 45 and whether it’s possible to achieve an output of 5. Suitable for students in Grades 7-9, covering function composition.

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