# To find the value of g − 1 ( 5 ) ### 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 2.7, Problem 24E
To determine

## To find the value of g−1(5)

Expert Solution

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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