Explanation The given logarithm function is, f ( x ) = log 3 ( x 2 − 4 x − 5 ) . The argument of the function f ( x ) = log 3 ( x 2 − 4 x − 5 ) is x 2 − 4 x − 5 . The domain of f is the set of all real numbers x such that x 2 − 4 x − 5 > 0 . Solve the equation x 2 − 4 x − 5 = 0 as follows. x 2 − 4 x − 5 = 0 x 2 − 5 x + x − 5 = 0 x ( x − 5 ) + 1 ( x − 5 ) = 0 ( x − 5 ) ( x + 1 ) = 0 x = 5 or x = − 1 Therefore, the values of x are 5 and − 1 . That is, the logarithmic function is not defined for the x values 5 and − 1 . Thus, the interval is ( − ∞ , − 1 ) , ( − 1 , 5 ) and ( 5 , ∞ ) . Construct a table and check for the intervals where the function y = x 2 − 4 x − 5 is positive and negative as shown in the below Table

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ISBN: 9780321880116

Author: Michael Sullivan III, Katherine R. Struve, Janet Mazzarella

Publisher: PEARSON

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Chapter 11.3, Problem 115E

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The domain of logarithm function f(x)=log3(x2−4x−5).

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Chapter 11.3, Problem 114E

Chapter 11.3, Problem 116E

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Chapter 11 Solutions

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Ch. 11.1 - Given two functions f and g, the ____ ____,...Ch. 11.1 - Prob. 2E Ch. 11.1 - Prob. 3E Ch. 11.1 - Prob. 4E Ch. 11.1 - Prob. 5E Ch. 11.1 - Prob. 6E Ch. 11.1 - Prob. 7E Ch. 11.1 - Prob. 8E Ch. 11.1 - Prob. 9E Ch. 11.1 - Prob. 10E

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The domain of logarithm function f ( x ) = log 3 ( x 2 − 4 x − 5 ) .

Solution Summary: The author explains the domain of the logarithm function f(x)=mathrmlog_3 (x

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The domain of logarithm function f(x)=log3(x2−4x−5).

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