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6th Edition

Stewart + 5 others

Publisher: Cengage Learning

ISBN: 9780840068071

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.

**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*,

*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

Substitute different inputs *x* in function *.*

The outputs of these two inputs are

From the above mentioned definition,

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.