# The value of f ∘ g .

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

#### Solutions

Chapter T, Problem 7CDT

a)

To determine

## To find: The value of f∘g.

Expert Solution

The value of fg is 4x28x+2.

### Explanation of Solution

Given;

The functions are f(x)=x2+2x1 and g(x)=2x3.

Calculation:

Consider the given functions f(x)=x2+2x1 and g(x)=2x3.

The composition of the functions is,

fg=f(g(x))

Substitute g(x)=2x3 in f(g(x)) to find the value of fg,

f(g(x))=f(2x3)

Substitute x=2x3 in f(x)=x2+2x1 to find the value of f(2x3),

f(2x3)=(2x3)2+2×(2x3)1=4x212x+9+4x61=4x28x+2

Thus, the value of fg is 4x28x+2.

b)

To determine

### To find: The value of g∘f.

Expert Solution

The value of gf is 2x2+4x5.

### Explanation of Solution

Given;

The functions are f(x)=x2+2x1 and g(x)=2x3.

Calculation:

Consider the given functions f(x)=x2+2x1 and g(x)=2x3.

The composition of the functions is,

gf=g(f(x))

Substitute g(x)=2x3 in g(f(x)) to find the value of gf,

g(f(x))=g(x2+2x1)

Substitute x=x2+2x1 in g(x)=2x3 to find the value of g(x2+2x1),

g(x2+2x1)=2(x2+2x1)3=2x2+4x23=2x2+4x5

Thus, the value of gf is 2x2+4x5.

c)

To determine

### To find: The value of g∘g∘g.

Expert Solution

The value of ggg is 8x21.

### Explanation of Solution

Given;

The functions are f(x)=x2+2x1 and g(x)=2x3.

Calculation:

Consider the given functions f(x)=x2+2x1 and g(x)=2x3.

The composition of the functions is,

ggg=g(g(g(x)))

Substitute g(x)=2x3 in f(g(x)) to find the value of ggg,

g(g(g(x)))=g(g(2x3))

Substitute x=2x3 in g(x)=2x3 to find the value of g(2x3),

g(2x3)=2(2x3)3=4x63=4x9

Substitute x=2x3 in g(x)=2x3 to find the value of g(4x9),

g(4x9)=2(4x9)3=8x183=8x21

Thus, the value of ggg is 8x21.

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