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Consider two function machines that are placed as shown to the right. In parts (a) through (e), find the final output for each of the inputs. For part (f), find all g(x)=2x x for which (fog)(x)=x. a. Find the final output for 4. The final output is . (Type an integer or a simplified fraction.) b. Find the final output for √7. The final output is. (Type an exact answer, using radicals as needed.) c. Find the final output for 12. The final output is. (Type an integer or a simplified fraction.) d. Find the final output for n. The final output is e. Find the final output for 10 9- The final output is f. Find all x for which (fog)(x) = x. When x = (Type an integer or a simplified fraction.) g(x) (fog)(x) = x. (Type an integer or a simplified fraction.) f(x)=x-2 (fog)(x)

Consider two function machines that are placed as shown to the right. In parts (a) through (e), find the final output for each of the inputs. For part (f), find all g(x)=2x x for which (fog)(x)=x. a. Find the final output for 4. The final output is . (Type an integer or a simplified fraction.) b. Find the final output for √7. The final output is. (Type an exact answer, using radicals as needed.) c. Find the final output for 12. The final output is. (Type an integer or a simplified fraction.) d. Find the final output for n. The final output is e. Find the final output for 10 9- The final output is f. Find all x for which (fog)(x) = x. When x = (Type an integer or a simplified fraction.) g(x) (fog)(x) = x. (Type an integer or a simplified fraction.) f(x)=x-2 (fog)(x)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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### Function Machines and Composition of Functions Consider two function machines that are placed as shown below. For parts (a) through (e), find the final output for each of the inputs. For part (f), find all \( x \) for which \( (f \circ g)(x) = x \). #### Diagram Explanation: The diagram shows two function machines connected sequentially: 1. The first function \( g(x) \) is defined as \( g(x) = 2x \). 2. The output of \( g(x) \) is then used as the input for the second function \( f(x) \), defined as \( f(x) = x - 2 \). The task is to find the final output after the input passes through both functions, i.e., to find \( f(g(x)) \). --- #### Problem Set: **a. Find the final output for \( x = 4 \).** **The final output is \( \boxed{\_\_\_} \).** (Type an integer or a simplified fraction.) --- **b. Find the final output for \( x = \sqrt{7} \).** **The final output is \( \boxed{\_\_\_} \).** (Type an exact answer, using radicals as needed.) --- **c. Find the final output for \( x = 12 \).** **The final output is \( \boxed{\_\_\_} \).** (Type an integer or a simplified fraction.) --- **d. Find the final output for \( x = n \).** **The final output is \( \boxed{\_\_\_} \).** --- **e. Find the final output for \( x = \frac{10}{9} \).** **The final output is \( \boxed{\_\_\_} \).** (Type an integer or a simplified fraction.) --- **f. Find all \( x \) for which \( (f \circ g)(x) = x \).** **When \( x = \boxed{\_\_\_} \), \( (f \circ g)(x) = x \).** (Type an integer or a simplified fraction.)
Transcribed Image Text:### Function Machines and Composition of Functions Consider two function machines that are placed as shown below. For parts (a) through (e), find the final output for each of the inputs. For part (f), find all \( x \) for which \( (f \circ g)(x) = x \). #### Diagram Explanation: The diagram shows two function machines connected sequentially: 1. The first function \( g(x) \) is defined as \( g(x) = 2x \). 2. The output of \( g(x) \) is then used as the input for the second function \( f(x) \), defined as \( f(x) = x - 2 \). The task is to find the final output after the input passes through both functions, i.e., to find \( f(g(x)) \). --- #### Problem Set: **a. Find the final output for \( x = 4 \).** **The final output is \( \boxed{\_\_\_} \).** (Type an integer or a simplified fraction.) --- **b. Find the final output for \( x = \sqrt{7} \).** **The final output is \( \boxed{\_\_\_} \).** (Type an exact answer, using radicals as needed.) --- **c. Find the final output for \( x = 12 \).** **The final output is \( \boxed{\_\_\_} \).** (Type an integer or a simplified fraction.) --- **d. Find the final output for \( x = n \).** **The final output is \( \boxed{\_\_\_} \).** --- **e. Find the final output for \( x = \frac{10}{9} \).** **The final output is \( \boxed{\_\_\_} \).** (Type an integer or a simplified fraction.) --- **f. Find all \( x \) for which \( (f \circ g)(x) = x \).** **When \( x = \boxed{\_\_\_} \), \( (f \circ g)(x) = x \).** (Type an integer or a simplified fraction.)
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