Explanation Given information : The function f ( x ) = x + a x − 1 , where constant a ≠ 1 Concept Involved: The steps to convert function to its inverse are as follows: Step 1: Replace f ( x ) with x Step 2: Interchange x as y and y as x Step 3: Solve the equation for y , which is undo whatever is done to y to get it in one side of the equation. Step 4: Replace y with f − 1 ( x ) Calculation: Description Steps Replace f ( x ) with x y = x + a x − 1 Interchange x as y and y as x x = y + a y − 1 Multiply y − 1 on both sides in an attempt of getting rid of the fraction x ( y − 1 ) = y + a ( y − 1 ) ⋅ ( y − 1 ) Cancel common factors in right side of the equation x ( y − 1 ) = y + a ( y − 1 ) ⋅ ( y − 1 ) Write the simplified equation without fraction x ( y − 1 ) = y + a

7th Edition

ISBN: 9781524916817

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

Publisher: Kendall Hunt Publishing

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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 61SP

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Toshow : the given function is its own inverse.

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Chapter 1, Problem 60SP

Chapter 1, Problem 62SP

Chapter 1 Solutions

Calculus

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Toshow : the given function is its own inverse.

Solution Summary: The author explains that the function f(x)=x+ax1 is its own inverse.

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Toshow : the given function is its own inverse.

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Chapter 1 Solutions