Explanation Given Information: It is provided a function f ( x ) = cot , x ∈ [ 0 , π ] . Calculation: In the above question it is provided a function f ( x ) = cot x , x ∈ [ 0 , π ] . if we look at any value of the input such as 10 then the function has exactly one y − c o o r d i n a t e when x = 10 ; that is the graph passes the vertical line test which means for every input there is only one output; The graph of the given function is given by: To check whether the given function has an inverse then the graph of the function should be one-to-one For this we use horizontal line test , in order to use horizontal line let’s just use the line y = 1 Since the line y = 1 intersects the graph of f ( x ) = cot x , x ∈ [ 0 , π ] at exactly one point then the given function is one-to-one as the function has exactly one input for every output , hence its inverse exists

Calculus: Special Edition: Chapters 1-5 (w/ WebAssign)

6th Edition

ISBN: 9781524908102

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Concept explainers

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:

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Chapter 1, Problem 40SP

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To find: f−1 using horizontal line test and sketch the graph if the inverse exists.

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Chapter 1, Problem 39SP

Chapter 1, Problem 41SP

Chapter 1 Solutions

Calculus: Special Edition: Chapters 1-5 (w/ WebAssign)

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f − 1 using horizontal line test and sketch the graph if the inverse exists.

Solution Summary: The author explains how to find f-1 using horizontal line test and sketch the graph if the inverse exists.

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To find: f−1 using horizontal line test and sketch the graph if the inverse exists.

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Chapter 1 Solutions