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4th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781337687805

Chapter 1, Problem 12RCC

(a)

To determine

**To explain:** The definition of one-to-one function.

Expert Solution

A function *f* is called one-to-one if every element of the range corresponds to exactly one element of the domain.

That is, if

In other words, a function is said to be one to one if every image as a unique pre image in the domain.

Graph is one-to-one if and only if every horizontal line intersect function *f* at most once.

Therefore, horizontal line must cross at only one point or it should be parallel to the graph.

(b)

To determine

**To define:** The inverse function *f* and explain the construction of the graph of the inverse

Expert Solution

**Solution:**

If the function *f* is one-to-one then the graph of *f* and graph of

**Given:**

Function *f* is a one-to-one function.

Let

Replace *x* by *y*

Take

Check whether the graph of the function *f* is one-to-one by the horizontal line test in order to find the graph of

If the function *f* is not one-to-one then

If the function *f* is one-to-one then the graph of *f* and graph of