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 2.7, Problem 93E

a.

To determine

To solve: f

Expert Solution

Answer to Problem 93E

  f(x)=x2+6

Explanation of Solution

Given information:

  g(x)=2x+1

  h(x)=4x2+4x+7

  fg=h

Concept used:

  fI=If=f

  ff1=f1f=I

Calculation:

  fg=hfgg1=hg1       [Compose of g1 from the right]fI=hg1f=hg1

  g(x)=2x+1y=2x+12x=y1x=y12g1(y)=y12g1(x)=x12

We have, f=hg1

  f=hg1=h(g1)=h(x12)=4(x12)2+4(x12)+7=(x1)2+2(x1)+7=x22x+1+2x2+7=x2+6

b.

To determine

To solve: g

Expert Solution

Answer to Problem 93E

  g(x)=x2+x1

Explanation of Solution

Given information:

  f(x)=3x+5

  h(x)=3x2+3x+2

  fg=h

Concept used:

  fI=If=f

  ff1=f1f=I

Calculation:

  fg=hf1fg=f1h       [Compose of g1 from the left]Ig=f1h g=f1h 

  f(x)=3x+5y=3x+53x=y5x=y53f1(y)=y53f1(x)=x53

We have, g=f1h 

  g=f1h=f1(h(x))=f1(3x2+3x+2)=(3x2+3x+2)53=3x2+3x+253=3x2+3x33=x2+x1

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