BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071
BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

Solutions

Chapter 2, Problem 12RCC

a.

To determine

To explain what a one to one function is.

Expert Solution

Answer to Problem 12RCC

A function with domain A is called a one-to-one function if no two elements of A have the same image, that is, f(x1)f(x2) whenever x1x2 

Explanation of Solution

Given:

The expression one to one function is given.

Concept Used:

The concept of one to one functions is used.

A function with domain A is called a one-to-one function if no two elements of A have the same image, that is, f(x1)f(x2) whenever x1x2 

b.

To determine

To explain how we can tell from graph of a function whether it is one to one.

Expert Solution

Answer to Problem 12RCC

If the graph of a function f is known, it is easy to determine if the function is one to one. Use the Horizontal Line Test. If no horizontal line intersects the graph of the function f in more than one point, then the function is one to one.

 

Explanation of Solution

Given:

The expression one to one function is given.

Concept Used:

The concept of one to one functions is used.

If the graph of a function f is known, it is easy to determine if the function is one to one. Use the Horizontal Line Test. If no horizontal line intersects the graph of the function f in more than one point, then the function is one to one.

c.

To determine

To define f1 and tell its domain and range.

Expert Solution

Answer to Problem 12RCC

The inverse function f1 is defined as f:f1(f(x))=x . The Domain of f1 = B and the Range of f1 =A.

Explanation of Solution

Given:

The expression of inverse function f1 of function f is given.

Concept Used:

The concept of inverse functions is used.

The inverse function f1 is defined as f:f1(f(x))=x .

The Domain of f1 = the range of f = B. The Range of f1 = the domain of f = A.

d.

To determine

To explain how to find the formula of f1 if formula of f is given.

Expert Solution

Answer to Problem 12RCC

The steps to find out the formula of f1 is given below.

1. Write y=f(x).

2. Solve this equation for x in terms of y (if possible).

3. Interchange x and y. The resulting equation is y=f1(x) .

Explanation of Solution

Given:

The expression of inverse function f1 of functionf is given.

Concept Used:

The concept of inverse functions is used.

1. Write y=f(x).

2. Solve this equation for x in terms of y (if possible).

3. Interchange x and y. The resulting equation is y=f1(x) .

e.

To determine

To explain how to plot the graph of f1 if graph of f is given.

Expert Solution

Answer to Problem 12RCC

The graph of f1 is obtained by reflecting the graph of f in the line y = x .

Explanation of Solution

Given:

The graph of function f is given.

Concept Used:

The concept of inverse functions is used.

The graph of f1 is obtained by reflecting the graph of f in the line y = x .

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