For Problems 1 − 18 , determine ( f ∘ g ) ( x ) .and ( g ∘ f ) ( x ) for each pair of functions. Also specify the domain of ( f ∘ g ) ( x ) and ( g ∘ f ) ( x ) . ( Objective 1 ) f ( x ) = 1 x and g ( x ) = 1 x − 4

Q: Expert Answer

To determine To find: The composition functions and domain of the given pair of functions. f ( x ) = 1 x and g ( x ) = 1 x − 4 Explanation Approach: The composition of functions is the process of combining two functions where one function is performed first and the result of which is substituted in place of each x in the other function. The composition of functions f and g is defined by ( f ∘ g ) ( x ) = f ( g ( x ) ) for all x in the domain of g such that g ( x ) is the domain of f . Procedure: To find the domain of the function, Equating the denominator equal to zero and then find the value of variable. The set of domain of the function is all real number except the finding values. Calculation: Consider the given function for f ( x ) , f ( x ) = 1 x …… ( 1 ) Consider the given function for g ( x ) , g ( x ) = 1 x − 4 ……. ( 2 ) The composition of function is, ( f ∘ g ) ( x ) = f ( g ( x ) ) Substitute g ( x ) for x in equation ( 1 ) . ( f ∘ g ) ( x ) = f ( g ( x ) ) = f ( 1 x − 4 ) = 1 ( 1 x − 4 ) = x − 4 Thus, the composition function is, ( f ∘ g ) ( x ) = x − 4 The domain of function is given by, D = ( − ∞ , 4 ) ∪ ( 4 , ∞ ) Substitute f ( x ) for x in equation ( 2 )

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Answer 1

BuyFind

Intermediate Algebra

10th Edition

Jerome E. Kaufmann + 1 other

Publisher: Cengage Learning

ISBN: 9781285195728

Solutions

Chapter

Section

Answer 2

BuyFind

Intermediate Algebra

10th Edition

Jerome E. Kaufmann + 1 other

Publisher: Cengage Learning

ISBN: 9781285195728

Solutions

Chapter

Section

Answer 3

Solutions

Chapter

Section

Answer 4

Chapter

Section

Answer 5

To determine

To find:

The composition functions and domain of the given pair of functions.

f(x)=1x and g(x)=1x−4

Explanation of Solution

Approach:

The composition of functions is the process of combining two functions where one function is performed first and the result of which is substituted in place of each x in the other function.

The composition of functions f and g is defined by (f∘g)(x)=f(g(x)) for all x in the domain of g such that g(x) is the domain of f.

Procedure:

To find the domain of the function,

Equating the denominator equal to zero and then find the value of variable. The set of domain of the function is all real number except the finding values.

Calculation:

Consider the given function for f(x),

f(x)=1x……(1)

Consider the given function for g(x),

g(x)=1x−4……. (2)

The composition of function is,

(f∘g)(x)=f(g(x))

Substitute g(x) for x in equation (1).

(f∘g)(x)=f(g(x))=f(1x−4)=1(1x−4)=x−4

Thus, the composition function is,

(f∘g)(x)=x−4

The domain of function is given by,

D=(−∞,4)∪(4,∞)

Substitute f(x) for x in equation (2)

For Problems 1 − 18 , determine ( f ∘ g ) ( x ) .and ( g ∘ f ) ( x ) for each pair of functions. Also specify the domain of ( f ∘ g ) ( x ) and ( g ∘ f ) ( x ) . ( Objective 1 ) f ( x ) = 1 x and g ( x ) = 1 x − 4

Intermediate Algebra

Solutions

Intermediate Algebra