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 31E

(a)

To determine

To find: The inverse of the function f(x)=1x2,0x1 ; how f1 is related to f.

Expert Solution

Answer to Problem 31E

The inverse of the function f(x)=1x2,0x1 is f1(x)=1x2 and f1=f .

Explanation of Solution

Let the given function as y=1x2 .

Solve this equation for x as follows.

y=1x2y2=1x21y2=x2x=±1y2

Interchange x and y and obtain the inverse function, y=±1x2 . Since the given function f(x)=4x+3 has the restriction as 0x1 , ignore the negative root of x.

Thus, the required inverse function is f1(x)=1x2 .

Observe that the given function and its inverse are the same. That is f1=f .

(b)

To determine

To identify: The graph of f and relate the answer with part (a).

Expert Solution

Explanation of Solution

The graphs of f(x)=1x2,0x1 is shown below in Figure 1.

Single Variable Calculus: Concepts and Contexts, Enhanced Edition, Chapter 1.6, Problem 31E

From Figure 1, it is observed that the graph of f(x)=1x2,0x1 is a reflection of the graph f1(x)=1x2 about the line y=x . Notice that the graphs of f1(x) and f(x) are same.

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