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6th Edition

Stewart + 5 others

Publisher: Cengage Learning

ISBN: 9780840068071

Chapter 2.7, Problem 90E

To determine

**To find**: The condition for the slope of a linear function to be one-to-one. To find the inverse of a linear one-to-one function and its slope.

Expert Solution

A linear function

The inverse of the given

Yes, the inverse of the given function linear.

The slope of the inverse function is

**Given information**: A linear function

**Concept used**:

The linear function can be written as

A function with domain A is called a one-to one function if no two elements of A have the same image, that is

To be one-to-one the function should not have any repeated value horizontally.

If

**Calculation**:

The linear function is

To be one-to-one the function should not have any repeated value horizontally.

Since, the given function is linear; to be one-to-one it should not be a line parallel to X-axis.

The slope of a line parallel to x-axis is

So, to be a one-to-one function the slope have to be not equal to

Let,

Therefore, the inverse of the given

Yes, the inverse of the given function linear as it can be written in the form of

The slope of the inverse function is