Explanation The function is f ( x ) = 72 x 2 − 4 x − 21 . Principle used: If the product of two algebraic expressions is zero, then at least one of the factors is equal to zero. That is If A B = 0 , then A = 0 or B = 0 . Procedure used: 1 . Find an equivalent inequality with P ( x ) on one side and 0 on the other. 2. Change the inequality symbol to an equals sign and solve the related equation; that is, solve P ( x ) = 0 . 3. Use the solutions to divide the x axis into intervals. Then select a test value from each interval and determine the sign of the polynomial on the interval. 4. Determine the intervals for which the inequality is satisfied and write intervals notation or set builder notation for the solution set. Include the endpoints of the intervals in the solution set if the inequality symbol is ≤ or ≥ . Calculation: The function is f ( x ) = 72 x 2 − 4 x − 21 . Since the square of any function can never be negative, the radicand x 2 − 4 x − 21 > 0 . Change the inequality sign by equal sign to form equivalent equation as x 2 − 4 x − 21 = 0 . In order to find the domain of the radical function, first equate the radicand to zero and simplify for x . x 2 − 4 x − 21 = 0 x 2 − 7 x + 3 x − 21 = 0 x ( x − 7 ) + 3 ( x − 7 ) = 0 ( x + 3 ) ( x − 7 ) = 0 On further simplification, ( x − 7 ) = 0 or ( x + 3 ) = 0 x = 7 or x = − 3 The solution set is { − 3 , 7 } . The solutions divide the x axis into the intervals as ( − ∞ , − 3 ) , ( − 3 , 7 ) and ( 7 , ∞ ) . Find the sign of the polynomial on each interval by selecting test value as follows. Let the polynomial function denoted by g ( x ) = x 2 − 4 x − 21

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ISBN: 2810000027802

Author: BITTINGER

Publisher: PEARSON

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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 4.6, Problem 95E

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The domain of the function f(x)=72x2−4x−21.

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Chapter 4.6, Problem 94E

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The domain of the function f ( x ) = 72 x 2 − 4 x − 21 .

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