# To explain what a one to one function is.

### Precalculus: Mathematics for Calcu...

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

### 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

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

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 f−1 and tell its domain and range.

Expert Solution

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 f−1 if formula of f is given.

Expert Solution

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 f−1 if graph of f is given.

Expert Solution

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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