# the formula for the inverse of the function f ( x ) = 4 x − 1 2 x + 3 .

### 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 22E
To determine

## To find: the formula for the inverse of the function f(x)=4x−12x+3 .

Expert Solution

The formula for the inverse of the function f(x)=4x12x+3 is f1(x)=3x+12x4 .

### Explanation of Solution

Let the given function as y=4x12x+3 .

Solve this equation for x as follows.

y(2x+3)=4x12xy+3y=4x12xy4x=13yx(2y4)=(3y+1)

Therefore, the value of x=3y+12y4 .

Interchange x and y and obtain the inverse function, y=3x+12x4 .

Thus, the required inverse function is f1(x)=3x+12x4 .

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