# Determine whether the given function g ( x ) = 2 − 2 x + x 2 is one −to − one.

### 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, Problem 82RE
To determine

Expert Solution

## Answer to Problem 82RE

Hence, g is not one −to − one.

### Explanation of Solution

Given information: Consider the function g(x)=22x+x2

Calculation:

Suppose that the numbers x1 and x2 such that g(x1)=g(x2) then,

22x1+x1222x2+x222x1+x122x2+x22x1(2x1)x2(2x2)             x1x2

Recall the definition of one −to − one, suppose that the numbers x1 and x2 such that g(x1)=g(x2)x1=x2

Hence, g is not one −to − one.

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