BuyFind

Precalculus: Mathematics for Calcu...

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

Precalculus: Mathematics for Calcu...

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

Solutions

Chapter 2.6, Problem 24E

a.

To determine

To evaluate the expression.

Expert Solution

Answer to Problem 24E

The expression is evaluated as:

  (ff)(2)=38

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,

  (ff)(x)=f(f(x))

Substitute, f(x)=3x5 ,

  (ff)(x)=f(3x5)(ff)(x)=3(3x5)5(ff)(x)=9x155(ff)(x)=9x20 [since, f(x)=3x5 ]

Now, substitute, x=1 ,

  (ff)(1)=9(1)20(ff)(1)=920(ff)(1)=29

Hence,

The expression is evaluated as:

  (ff)(1)=29

b.

To determine

To evaluate the expression.

Expert Solution

Answer to Problem 24E

The expression is evaluated as:

  (gg)(x)=1

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,

  (gg)(x)=g(g(x))

Substitute, g(x)=2x2 ,

  (gg)(x)=g(2x2)(gg)(x)=2(2x2)2(gg)(x)=2(44x2+x4)(gg)(x)=24+4x2x4(gg)(x)=2+4x2x4 [since, g(x)=2x2 ]

Now, substitute, x=1 ,

  (gg)(x)=2+4(1)2(1)4(gg)(x)=2+41(gg)(x)=1

Hence,

The expression is evaluated as:

  (gg)(x)=1

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