# The inverse of the given function and sketch the graph of function and its inverse.

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

#### Solutions

Chapter 1.6, Problem 28E
To determine

## To find: The inverse of the given function and sketch the graph of function and its inverse.

Expert Solution

The inverse of the given function is f1(x)=ln(2x) .

### Explanation of Solution

Given information:

The given function is,

f(x)=2ex

The inverse of the given function is calculated as,

f(x)=2exy=2exex=2ylnex=ln(2y)

Simplify further,

x=ln(2y)

For the inverse of the function, interchange x and y ,

y=ln(2x)f1(x)=ln(2x)

Consider the graph of the function and its inverse as follows,

Therefore, the inverse of the given function is f1(x)=ln(2x) and the graph of f and f1 are reflection about the line.

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