# The inverse of the given function.

### 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 26E
To determine

## To find: The inverse of the given function.

Expert Solution

The inverse of the given function is f1(x)=ln(x12x) .

### Explanation of Solution

Given information:

The given function is,

y=ex1+2ex

The inverse of the given function is calculated as,

y=ex1+2exy(1+2ex)=exy+2yex=ex2yexex=y

Simplify further,

ex(2y1)=yex=y12ylnex=ln(y12y)x=ln(y12y)

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

y=ln(x12x)f1(x)=ln(x12x)

Therefore, the inverse of the given function is f1(x)=ln(x12x)

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