Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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**Function Machines and Outputs**

Consider the two function machines that are placed as shown. Find the final output for each of the following inputs:

Inputs: 
a. 6
b. 10
c. \(\sqrt{10}\)
d. 0
e. \(\frac{5}{8}\)
f. \(n\)

**Image Explanation:**

The diagram on the right consists of two function machines connected in sequence. 

1. The first machine represents the function \( f(x) = 10x \).
2. The output of the first machine, \( f(x) \), is then the input for the second machine, which represents the function \( g(x) = x - 3 \).
3. The final output is represented as \( g(f(x)) \). 

**Outputs:**

a. The output for 6 is [____].\
(Type an integer or a simplified fraction.)

b. The output for 10 is [____].\
(Type an integer or a simplified fraction.)

c. The output for \(\sqrt{10}\) is [____].\
(Type an exact answer, using radicals as needed.)

d. The output for 0 is [____].\
(Type an integer or a simplified fraction.)

e. The output for \(\frac{5}{8}\) is [____].\
(Type an integer or a simplified fraction.)

f. The output for \(n\) is [____].\
(Simplify your answer.)

---

For additional explanations and practice questions, please refer to the function machine exercise section of our website.
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Transcribed Image Text:--- **Function Machines and Outputs** Consider the two function machines that are placed as shown. Find the final output for each of the following inputs: Inputs: a. 6 b. 10 c. \(\sqrt{10}\) d. 0 e. \(\frac{5}{8}\) f. \(n\) **Image Explanation:** The diagram on the right consists of two function machines connected in sequence. 1. The first machine represents the function \( f(x) = 10x \). 2. The output of the first machine, \( f(x) \), is then the input for the second machine, which represents the function \( g(x) = x - 3 \). 3. The final output is represented as \( g(f(x)) \). **Outputs:** a. The output for 6 is [____].\ (Type an integer or a simplified fraction.) b. The output for 10 is [____].\ (Type an integer or a simplified fraction.) c. The output for \(\sqrt{10}\) is [____].\ (Type an exact answer, using radicals as needed.) d. The output for 0 is [____].\ (Type an integer or a simplified fraction.) e. The output for \(\frac{5}{8}\) is [____].\ (Type an integer or a simplified fraction.) f. The output for \(n\) is [____].\ (Simplify your answer.) --- For additional explanations and practice questions, please refer to the function machine exercise section of our website.
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