# To find f ∘ g .

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

#### Solutions

Chapter 2, Problem 9T

a.

To determine

## To find f∘g.

Expert Solution

### Explanation of Solution

Given:

The expression of f(x) is given = f(x)=x2+1.

The expression of g(x) is given = g(x)=x3.

Concept Used:

The concept of composition of functions is used.

Calculation:

The expression of fg is,

fg=f(g(x))fg=f(x3) fg= (x3) 2 +1fg=x26x+9+1fg=x26x+10

Conclusion:

Hence, the answer is fg=x26x+10 .

b.

To determine

Expert Solution

### Explanation of Solution

Given:

The expression of f(x) is given = f(x)=x2+1.

The expression of g(x) is given = g(x)=x3.

Concept Used:

The concept of composition of functions is used.

Calculation:

The expression of gf is,

gf=g(f(x))gf=g(x2+1)gf=(x2+1)3gf=x22

Conclusion:

Hence, the answer is gf=x22 .

c.

To determine

Expert Solution

### Explanation of Solution

Given:

The expression of f(x) is given = f(x)=x2+1.

The expression of g(x) is given = g(x)=x3.

Concept Used:

The concept of composition of functions is used.

Calculation:

The expression of f(g(2)) is,

f(g(2))=f(23)f(g(2))=f(1) f(g(2))= (1) 2 +1f(g(2))=2

Conclusion:

c.

To determine

Expert Solution

### Explanation of Solution

Given:

The expression of f(x) is given = f(x)=x2+1.

The expression of g(x) is given = g(x)=x3.

Concept Used:

The concept of composition of functions is used.

Calculation:

The expression of g(f(2)) is,

g(f(2))=g( (2) 2 +1)g(f(2))=g(5)g(f(2))=53g(f(2))=2

Conclusion:

e.

To determine

Expert Solution

### Explanation of Solution

Given:

The expression of f(x) is given = f(x)=x2+1.

The expression of g(x) is given = g(x)=x3.

Concept Used:

The concept of composition of functions is used.

Calculation:

The expression of ggg. is,

ggg=g(g(g(x)))ggg=g(g(x3))ggg=g(x6)ggg=x9

Conclusion:

Hence, the answer is ggg=x9. .

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