# The inverse function of f ( x ) = 2 + x .

### 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 71E

a.

To determine

Expert Solution

## Answer to Problem 71E

f1(x)=x2

### Explanation of Solution

Given information:

f(x)=2+x

Concept Use: Let, f be a one-to-one function with domain A and range B. Then its inverse function f1 has domain B and range A and is defining by f1(y)=xf(x)=y for any y in B.

Calculation:

First, we replace f(x) with y ,

Then,

f(x)=2+xy=2+xy2=xx=y2f1(y)=y2f1(x)=x2

Thus, f1(x)=x2 .

b.

To determine

Expert Solution

### Explanation of Solution

Given information: f(x)=2+x and f1(x)=x2

Graph:

 x 0 1 2 −1 −2 f(x) 2 3 4 1 0

Interpretation:

A point on the graph of f(x) , (1,3) . The dotted line is the graph of y=x , CD is the graph of f1(x) . AB is the perpendicular on the dotted line from the point (1,3) , It intersects the CD line at point F (3,1) .

It is clear that the coordinate of E is reversed from F.

Thus, it means f(x) and f1(x) is the reflection of each other in the line y=x (Dotted line).

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