Explanation Approach: A function is relation in which every input is associated with a single output and there are many types of a function like, one-one, on-to etc. Calculation: Consider the two function machine given in the figure 11, in which bottom machine g ( x ) = 7 x is at the top and top machine f ( x ) = x − 1 is at the bottom. To compute the final output ( f ∘ g ) ( x ) . ( f ∘ g ) ( x ) = f ( g ( x ) ) = f ( 7 x ) = 7 x − 1 Next consider the inputs given in different parts of problem 11. (a) Consider the input x = 5 . To find ( f ∘ g ) ( x ) , substitute 5 for x in the final output. ( f ∘ g ) ( 5 ) = 7 ( 5 ) − 1 = 35 − 1 = 34 Therefore the final output of the two machines is ( f ∘ g ) ( 5 ) = 34 . b. Consider the input x = 3 . To find ( f ∘ g ) ( x ) , substitute 3 for x in the final output. ( f ∘ g ) ( 3 ) = 7 ( 3 ) − 1 = 7 3 − 1 Therefore the final output of the two machines is ( f ∘ g ) ( 3 ) = 7 3 − 1 To determine b. To find: The value of x for which ( f ∘ g ) ( x ) = x .

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Author: BOSCHMANS

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Chapter 8.3B, Problem 13A

To determine

a.

To find:

The final output (f∘g)(x) for the input when the bottom machine g(x)=7x is on top and the top machine f(x)=x−1.

To determine

b.

To find:

The value of x for which (f∘g)(x)=x.

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Chapter 8.3B, Problem 12A

Chapter 8.3B, Problem 14A

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a. To find: The final output ( f ∘ g ) ( x ) for the input when the bottom machine g ( x ) = 7 x is on top and the top machine f ( x ) = x − 1 .

Solution Summary: The author calculates the final output of a function machine given in the figure 11, in which bottom machine g(x)=7x is at the top and top machine

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a.

To find:

The final output (f∘g)(x) for the input when the bottom machine g(x)=7x is on top and the top machine f(x)=x−1.

b.

To find:

The value of x for which (f∘g)(x)=x.

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Chapter 8 Solutions

a. To find: The final output ( f ∘ g ) ( x ) for the input when the bottom machine g ( x ) = 7 x is on top and the top machine f ( x ) = x − 1 .

Solution Summary: The author calculates the final output of a function machine given in the figure 11, in which bottom machine g(x)=7x is at the top and top machine

Videos

a. To find: The final output (f∘g)(x) for the input when the bottom machine g(x)=7x is on top and the top machine f(x)=x−1.

b. To find: The value of x for which (f∘g)(x)=x.

Want to see the full answer?

Chapter 8 Solutions

a.

To find:

The final output (f∘g)(x) for the input when the bottom machine g(x)=7x is on top and the top machine f(x)=x−1.

b.

To find:

The value of x for which (f∘g)(x)=x.