BuyFind

Single Variable Calculus: Concepts...

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

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

Answer to Problem 28E

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,

  Single Variable Calculus: Concepts and Contexts, Enhanced Edition, Chapter 1.6, Problem 28E

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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