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 24E
To determine

To find: the formula for the inverse of the function y=x2x,x12 .

Expert Solution

Answer to Problem 24E

The formula for the inverse of the function y=x2x,x12 is f1(x)=12+x+14 .

Explanation of Solution

The given function is y=x2x .

Solve this equation for x as follows.

y+(12)2=x2x+(12)2[applying completing the square method]y+14=(x12)2y+14=±(x12)

Notice that the x is restricted as x12 and hence x120 .

Thus, ignore the negative root.

Then, y+14=x12 from which the value of x=12+y+14 .

Interchange x and y and obtain the inverse function, y=12+x+14 .

Thus, the required inverse function is f1(x)=12+x+14 .

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