# To evaluate the expression. ### 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 2.6, Problem 23E

a.

To determine

## To evaluate the expression.

Expert Solution

The expression is evaluated as:

(fg)(2)=11

### Explanation of Solution

Given information:

The functions are:

f(x)=3x5 and g(x)=2x2

Formula used:

The composition of the function is defined by,

(fg)(x)=f(g(x))

Calculation:

Use definition of composition of the function,

(fg)(x)=f(g(x))

Substitute, g(x)=2x2 ,

(fg)(x)=f(2x2)(fg)(x)=3(2x2)5(fg)(x)=63x25(fg)(x)=13x2 [since, f(x)=3x5 ]

Now, substitute, x=2 ,

(fg)(2)=13(2)2(fg)(2)=13(4)(fg)(2)=112(fg)(2)=11

Hence,

The expression is evaluated as:

(fg)(2)=11

b.

To determine

### To evaluate the expression.

Expert Solution

The expression is evaluated as:

(gf)(2)=119

### Explanation of Solution

Given information:

The functions are:

f(x)=3x5 and g(x)=2x2

Formula used:

The composition of the function is defined by,

(fg)(x)=f(g(x))

Calculation:

Use definition of composition of the function,

(gf)(x)=g(f(x))

Substitute, f(x)=3x5 ,

(gf)(x)=g(3x5)(gf)(x)=2(3x5)2(gf)(x)=2(9x230x+25)(gf)(x)=29x2+30x25(gf)(x)=9x2+30x23 [since, g(x)=2x2 ]

Now, substitute, x=2 ,

(gf)(2)=9(2)2+30(2)23(gf)(2)=9(4)+30(2)23(gf)(2)=366023(gf)(2)=119

Hence,

The expression is evaluated as:

(gf)(2)=119

### Have a homework question?

Subscribe to bartleby learn! Ask subject matter experts 30 homework questions each month. Plus, you’ll have access to millions of step-by-step textbook answers! 