# The type of outputs produced by different inputs of a one-to-one function f and informs the method of test which is used to prove that function f is a one-to-one function.

### 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 2.7, Problem 1E
To determine

## To fill: The type of outputs produced by different inputs of a one-to-one function f and informs the method of test which is used to prove that function f is a one-to-one function.

Expert Solution

A function f is one-to-one if different inputs produce different outputs and from the graph it can be proved that a function is one-to-one by using the Horizontal line Test.

### Explanation of Solution

Definitions used:

One-to-one function:

A function is said to be one-to-one if the range of the function corresponds to exactly one element of the domain.

In other words, for a one-to-one function f, f(a)f(b) if ab.

Horizontal line test:

In graph if one horizontal line does not intersect the graph of function more than once, then function f is one-to-one function and it is a Horizontal line test.

Calculation:

Let a function f is f(x),

Substitute different inputs x1 and x2 for x in function f(x).

The outputs of these two inputs are f(x1) and f(x2),

From the above mentioned definition, f(x1)f(x2).

Therefore, a function f is one-to-one if different inputs produce different outputs.

From the definition of horizontal line test, it is possible to determine if a function is one-to-one.

Thus, a function f is one-to-one if different inputs produce different outputs and from the graph it can be proved that a function is one-to-one by using the Horizontal line test.

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