# The inverse function of f ( x ) = 2 − 1 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 72E

a.

To determine

## To find: The inverse function of f(x)=2−12x .

Expert Solution

f1(x)=42x

### Explanation of Solution

Given information: f(x)=212x

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)=212xy=212xy=4x22y=4x2y4=xx=42yf1(y)=42yf1(x)=42x

Thus, f1(x)=42x .

b.

To determine

Expert Solution

### Explanation of Solution

Given information: f(x)=212x and f1(x)=42x

Graph:

 x 0 2 4 −2 −4 f(x) 2 1 0 3 4

Interpretation:

A point on the graph of f(x) , (0,2) . 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 (0,2) , It intersects the CD line at point F (2,0) .

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).

### Have a homework question?

Subscribe to bartleby learn! Ask subject matter experts 30 homework questions each month. Plus, you’ll have access to millions of step-by-step textbook answers!