a. Explanation Given information : The functions f ( x ) = 1 − e x 2 1 − e 1 − x 2 Concept Involved: Domain means the values of x that gives a defined output to the function. Whenever we are trying to find the domain of the function, we need to identify the restrictions on the domain. The domain of a rational function includes all real numbers except those that cause the denominator to equal zero . To find the domain of a function with a rational expression, set the denominator of the expression not equal to zero and solve for x using the zero product property which states that if a ⋅ b = 0 , then a = 0 or b = 0 . Calculation: Description Steps To find the restriction on the domain set the denominator not equal to zero and solve for x 1 − e 1 − x 2 ≠ 0 Subtract 1 on both sides of the equation 1 − e 1 − x 2 − 1 ≠ 0 − 1 Dividing by -1 on both sides and simplifying the fraction − e 1 − x 2 ≠ − 1 − e 1 − x 2 − 1 ≠ − 1 − 1 e 1 − x 2 ≠ 1 Taking natural logarithm on both sides ln e 1 − x 2 ≠ ln 1 Description Steps Applying the logarithmic property ln m n = n ln m in left side of the equation. Substituting the value of ln e = 1 & ln 1 = 0 ( 1 − x 2 ) ( ln e ) ≠ ln 1 ( 1 − x 2 ) ( 1 ) ≠ 0 1 − x 2 ≠ 0 Factor the left side of the equation 1 2 − x 2 ≠ 0 ( 1 − x ) ( 1 + x ) & b. To determine To find : the domain of the function

Bundle: Biocalculus: Calculus, Probability, And Statistics For The Life Sciences + Webassign Printed Access Card For Stewart/day's Biocalculus: Calculus For Life Sciences, 1st Edition, Multi-term

1st Edition

ISBN: 9781305779037

Author: James Stewart, Troy Day

Publisher: Cengage Learning

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Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.

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Chapter 1.4, Problem 19E

To determine

Tofind : the domain of the function

To determine

To find : the domain of the function

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Chapter 1.4, Problem 18E

Chapter 1.4, Problem 20E

Chapter 1 Solutions

Bundle: Biocalculus: Calculus, Probability, And Statistics For The Life Sciences + Webassign Printed Access Card For Stewart/day's Biocalculus: Calculus For Life Sciences, 1st Edition, Multi-term

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Tofind : the domain of the function

Solution Summary: The author explains that the domain of a rational function includes all real numbers except those that cause the denominator to equal zero.

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Tofind : the domain of the function

To find : the domain of the function

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Chapter 1 Solutions