Explanation Given Information: The function is h ( x ) = { 1 − x if x < 1 1 if x = 1 x + 2 if x > 1 . Formula used: Continuity of closed form function theorem: Every function that is closed is continuous on its domain. If lim x → a f ( x ) exists and f ( a ) is defined, then lim x → a f ( x ) = f ( a ) The function is discontinuous at point x = a , if either, a) The limit lim x → a f ( x ) does not exist or b) The limit lim x → a f ( x ) does exist but it’s not equal to f ( a ) . Where, ‘ a ’ is any real number. Calculation: Consider the function h ( x ) = { 1 − x if x < 1 1 if x = 1 x + 2 if x > 1 At x = 1 , the function changes from one closed-form to another. So, the point x = 1 is the only possible point for discontinuity or for a singular point

Finite Mathematics and Applied Calculus (MindTap Course List)

7th Edition

ISBN: 9781337274203

Author: Stefan Waner, Steven Costenoble

Publisher: Cengage Learning

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Chapter 10.3, Problem 86E

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To calculate: The singular points and points of discontinuity of the function h(x)={1−x if x<11 if x=1x+2 if x>1.

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Chapter 10.3, Problem 85E

Chapter 10.3, Problem 87E

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The singular points and points of discontinuity of the function h ( x ) = { 1 − x if x < 1 1 if x = 1 x + 2 if x > 1 .

Solution Summary: The author explains the Continuity of closed form function theorem: Every function that is closed is continuous on its domain.

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To calculate: The singular points and points of discontinuity of the function h(x)={1−x if x<11 if x=1x+2 if x>1.

Want to see the full answer?

Chapter 10 Solutions

The singular points and points of discontinuity of the function h ( x ) = { 1 − x if x &lt; 1 1 if x = 1 x + 2 if x &gt; 1 .

Solution Summary: The author explains the Continuity of closed form function theorem: Every function that is closed is continuous on its domain.

Concept explainers

Videos

To calculate: The singular points and points of discontinuity of the function h(x)={1−x if x<11 if x=1x+2 if x>1.

Want to see the full answer?

Chapter 10 Solutions

The singular points and points of discontinuity of the function h ( x ) = { 1 − x if x < 1 1 if x = 1 x + 2 if x > 1 .