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 25E

a.

To determine

To evaluate the expression.

Expert Solution

Answer to Problem 25E

The expression is evaluated as:

  (fg)(x)=3x2+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,

  (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 ]

Hence,

The expression is evaluated as:

  (fg)(x)=13x2

b.

To determine

To evaluate the expression.

Expert Solution

Answer to Problem 25E

The expression is evaluated as:

  (gf)(x)=9x2+30x23

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 ]

Hence,

The expression is evaluated as:

  (gf)(x)=9x2+30x23

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