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 24E
To determine

To find the value of g1(5)

Expert Solution

Answer to Problem 24E

The value of g1(5) is 1.

Explanation of Solution

Given is the function g(x)=x2+4x,x2

Calculation:

Since g(x)=x2+4x is a quadratic function

To find the inverse of a quadratic function,

First, complete the square of the quadratic equation

  x2+4x=y

  x2+4x+4=y+4

[ Add square of the half of the middle value, which isb ]

  (x+2)2 =y+4

  x+2=y+4 [ solve for x ]

  x=y+4 2

Now interchange x and y

  y=x+42

Which can be written as

  g1(x)=x+4 2

  g(1)(5)=(5+4)2 [ putx =5]

  =92

   =32

  =1

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