For Problems 27 − 38 , determine the indicated functional values. (Objective 2) If f ( x ) = − x 3 and g ( x ) = | 2 x + 4 | , find ( f ∘ g ) ( − 1 ) and ( g ∘ f ) ( − 3 ) .

Q: Expert Answer

To determine To find: The indicated functional values of ( f ∘ g ) ( − 1 ) and ( g ∘ f ) ( − 3 ) . Explanation Given: The given functions are, f ( x ) = − x 3 g ( x ) = | 2 x + 4 | Approach: The composition of function 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 and ( g ∘ f ) ( x ) = g ( f ( x ) ) , for all x in the domain of f such that f ( x ) is the domain of g . Calculation: The functions are given by, f ( x ) = − x 3 ...... ( 1 ) g ( x ) = | 2 x + 4 | ...... ( 2 ) The composition of function f and g is given by, ( f ∘ g ) ( x ) = f ( g ( x ) ) ...... ( 3 ) ( g ∘ f ) ( x ) = g ( f ( x ) ) ...... ( 4 ) Substitute | 2 x + 4 | for g ( x ) in equation ( 3 ) . …… ( 5 ) Substitute | 2 x + 4 | for x in equation ( 1 ) . f ( | 2 x + 4 | ) = − ( | 2 x + 4 | ) 3 From equation ( 3 ) . ( f ∘ g ) ( x ) = − ( | 2 x + 4 | ) 3 …… ( 6 ) Substitute − 1 for x in equation ( 6 )

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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 indicated functional values of (f∘g)(−1) and (g∘f)(−3).

Explanation of Solution

Given:

The given functions are,

f(x)=−x3

g(x)=|2x+4|

Approach:

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

Calculation:

The functions are given by,

f(x)=−x3...... (1)

g(x)=|2x+4|...... (2)

The composition of function f and g is given by,

(f∘g)(x)=f(g(x))...... (3)

(g∘f)(x)=g(f(x)) ...... (4)

Substitute |2x+4| for g(x) in equation (3).

……(5)

Substitute |2x+4| for x in equation (1).

f(|2x+4|)=−(|2x+4|)3

From equation (3).

(f∘g)(x)=−(|2x+4|)3……(6)

Substitute −1 for x in equation (6)

For Problems 27 − 38 , determine the indicated functional values. (Objective 2) If f ( x ) = − x 3 and g ( x ) = | 2 x + 4 | , find ( f ∘ g ) ( − 1 ) and ( g ∘ f ) ( − 3 ) .

Intermediate Algebra

Solutions

Intermediate Algebra