# 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 22E

a.

To determine

## To evaluate the expression

Expert Solution

The value of a is 16

### Explanation of Solution

Given:

Equation is f(x)=3x5  and  g(x)=2x2

Calculation:

f(4)=3(4)5=7       [substitute 4 into f(x)and solve]f(7)=3(7)5=16    [substitute answer of  f(4)value into f(x)]

Conclusion:

The value of f(f(4)) is 16.

b.

To determine

### To evaluate the expression

Expert Solution

The value of b is 47

### Explanation of Solution

Given:

Equation is f(x)=3x5  and  g(x)=2x2

Calculation:

Since the question is a composition function f(f(4)) , the next step is to substitute f(4) value into f(x) and solve .

g(3)=232=7             [substitute 3 into g(x) and solve] g(7)=2 (7) 2 =47        [substitute the answer from g(3) into g(x) to find the composition function g(g(3)) ]

Conclusion:

The value of b is 47

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