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 23E
To determine

To find: the formula for the inverse of the function f(x)=e2x1 .

Expert Solution

Answer to Problem 23E

The formula for the inverse of the function f(x)=e2x1 is f1(x)=lnx+12 .

Explanation of Solution

Let the given function as y=e2x1 .

Solve this equation for x as follows.

lny=lne2x1lny=2x1lny+1=2xx=lny+12

Then, interchange x and y and obtain the inverse function, y=lnx+12 .

Thus, the required inverse function is f1(x)=lnx+12 .

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